Professor  A.   0.  Leuschner 
1868-1953 


Gift  of 
Dr.Erida  Leuschner  Rei chert 


Great  Double  Telescope,  Visual  and  Photographic,  of  the  Potsdam 
Astrophysical  Observatory.     (See  Sec.  51.) 


MANUAL  OF  ASTRONOMY 


A   TEXT-BOOK 


BY 


CHARLES  A.  (YOUNG,  PH.D.,  LL.D. 

LATE  PROFESSOR  OF  ASTRONOMY  IN  PRINCETON  UNIVERSITY 

AUTHOR  OF  "  THE  SUN  "  AND  OF  A  SERIES  OF 

ASTRONOMICAL  TEXT-BOOKS 


GINN  AND  COMPANY 

BOSTON     •    NEW   YORK     •    CHICAGO     •    LONDON 
ATLANTA     •    DALLAS     •    COLUMBUS     •    SAN   FRANCISCO 


ENTERED  AT  STATIONERS'  HAT/T, 


COPYRIGHT,  1902 
BY  CHARLES  A.  YOUNG 


ALL  RIGHTS  RESERVED 
224.1 


GIFT 


(gftc   athenaeum   jgregg 

G1NN  AND  COMPANY  •  PRO- 
PRIETORS  •  BOSTON  •  U.S.A. 


PEEFACE 

THE  present  volume  has  been  prepared  in  response  to  a 
rather  pressing  demand  for  a  text-book  intermediate  between 
the  author's  Elements  of  Astronomy  and  his  Greneral  Astronomy. 
The  latter  is  found  by  many  teachers  to  be  too  large  for 
convenient  use  in  the  time  at  their  disposal,  while  the  former 
is  not  quite  sufficiently  extended  for  their  purpose. 

The  material  of  the  new  book  has  naturally  been  derived 
largely  from  its  predecessors;  but  everything  has  been  care- 
fully worked  over,  rearranged  and  rewritten  where  necessary, 
and  changed  and  added  to  in  order  to  bring  it  thoroughly 
up  to  date. 

The  writer  is  under  great  obligations  to  many  persons  who 
have  assisted  him  in  various  ways,  especially  to  Professor 
Anne  S.  Young,  of  the  astronomical  department  in  Mt. 
Holyoke  College,  who  has  carefully  read  and  corrected  all  the 
proof.  He  is  greatly  indebted  also  to  D.  Appleton  &  Co.  for 
permission  to  use  illustrations  from  The  Sun,  to  Warner  & 
Swasey  for  photographs  of  astronomical  instruments,  and  to 
numerous  other  friends  who  have  kindly  furnished  material  for 
engravings.  Among  these  may  be  mentioned  specially  Pro- 
fessor Pickering  of  the  Harvard  Observatory,  the  lamented 
Keeler,  and  Professors  Campbell  and  Hussey  of  the  Lick 

i" 

Ss880816 


iv  PREFACE 

Observatory,  and  Professors  Hale,  Frost,  and  Barnard  of  the 
Yerkes,  besides  several  others  to  whom  acknowledgment  is 
made  in  the  text. 

The    volume    speaks   for  itself   as    to    the    skillful   care    of 
printers  and  publishers  in  securing  the  most  perfect  mechan- 

ical execution. 

C.  A.  YOUNG 

PRINCETON,  N.J. 


PREFACE  TO  ISSUE  OF  1912 

IN  the  present  issue  a  number  of  more  or  less  important 
errata  have  been  corrected,  and  various  changes  and  additions 
nave  been  made,  required  by  the  recent  rapid  progress  of 

.TLB889 

astronomy. 
•^Irrguo 

MAY,  1912 

orfv/  an 


n 

Ilfl 

.oO 

i9ni 

bnii 


TABLE    OF   CONTENTS 


PAGES 

INTRODUCTION 1-5 

CHAPTER  I.  —  PRELIMINARY  CONSIDERATIONS  AND  DEFINI- 
TIONS  —  Fundamental  Notions  and  Definitions  —  Astronom- 
ical Coordinates  and  th«  "  Doctrine  of  the  Sphere  "  -  -  The 
Celestial  Globe  —  Exercises 6-31 

CHAPTER  II.  —  ASTRONOMICAL  INSTRUMENTS  —  Telescopes, 
and  their  Accessories  and  Mountings  —  Timekeepers  and 
Chronographs  —  The  Transit-Instrument  —  The  Prime  Ver- 
tical Instrument  —  The  Almucantar  —  The  Meridian-Circle 
and  Universal  Instrument  —  The  Micrometer  —  The  Heliom- 
eter  —  The  Sextant  —  Exercises 32-65 

CHAPTER  III.  —  CORRECTIONS  TO  ASTRONOMICAL  OBSER- 
VATIONS —  Dip  of  the  Horizon  —  Parallax  —  Semidiameter 

—  Refraction  —  Twinkling   or    Scintillation  —  Twilight  — 
Exercises 66-75 

CHAPTER  IV.  —  FUNDAMENTAL  PROBLEMS  OF  PRACTICAL 
ASTRONOMY  —  Latitude  —  Time  —  Longitude  —  Azimuth 

—  The   Right   Ascension  and  Declination  of   a   Heavenly 

Body  — Exercises 76-104 

CHAPTER   V.  —  THE  EARTH  AS  AN  ASTRONOMICAL  BODY  — 
Its  Form,  Rotation,  and  Dimensions  —  Mass,  Weight,  and 
Gravitation  —  The  Earth's  Mass  and  Density  —  Exercises    .  105-135 
CHAPTER  VI.  —  THE   ORBITAL   MOTION   OF   THE   EARTH  - 
The  Apparent  Motion  of  the   Sun  and  the  Ecliptic  —  The 
Orbital  Motion  of  the  Earth  —  Precession  and  Nutation  — 
Aberration  —  The  Equation  of  Time  —  The  Seasons  and  the 

Calendar  —  Exercises 136-165 

CHAPTER  VII. —  THE  MOON  — The  Moon's  Orbital  Motion 
and  the  Month  —  Distance,  Dimensions,  Mass,  Density,  and 
Force  of  Gravity  —  Rotation  and  Librations  —  Phases  — 
Light  and  Heat — Physical  Condition  —  Telescopic  Aspect 
and  Peculiarities  of  the  Lunar  Surface  .  ...  166-194 


vi  TABLE   OF   CONTENTS 

PAGES 

CHAPTER  VIII.  —  THE  SUN  —  Its  Distance,  Dimensions, 
Mass,  and  Density  —  Its  Rotation  and  Equatorial  Accel- 
eration—  Methods  of  studying  its  Surface  —  The  Photo- 
sphere—  Sun-Spots  —  Their  Nature,  Dimensions,  Develop- 
ment, and  Motions  —  Their  Distribution  and  Periodicity  — 
Sun-Spot  Theories 195-216 

CHAPTER  IX. —  THE  SUN  (Continued)  —  The  Spectroscope, 
the  Solar  Spectrum,  and  the  Chemical  Constitution  of 
the  Sun  —  The  Doppler-Fizeau  Principle — The  Chromo- 
sphere and  Prominences  —  The  Corona  —  The  Sun's 
Light  —  Measurement  of  the  Intensity  of  the  Sun's  Heat  — 
Theory  of  its  Maintenance  —  The  Age  and  Duration  of 
the  Sun  —  Summary  as  to  the  Constitution  of  the  Sun  — 
Exercises 217-260 

CHAPTER  X.  —  ECLIPSES  —  Form  and  Dimensions  of  Shad- 
ows —  Eclipses  of  the  Moon  —  Solar  Eclipses  —  Total, 
Annular,  and  Partial  —  Ecliptic  Limits  and  Number  of 
Eclipses  in  a  Year  —  Recurrence  of  Eclipses  and  the  Saros 

—  Occupations 261-274 

CHAPTER   XL  —  CELESTIAL     MECHANICS —  The     Laws     of 

Central  Force  —  Circular  Motion  —  Kepler's  Laws,  and  New- 
ton's Verification  of  the  Theory  of  Gravitation  —  The  Conic 
Sections  —  The  Problem  of  Two  Bodies  —  The  Parabolic 
Velocity  —  Exercises  —  The  Problem  of  Three  Bodies  and 
Perturbations  —  The  Tides 275-310 

CHAPTER  XII.  —  THE  PLANETS  IN  GENERAL — Bode's  Law 
—  The  Apparent  Motions  of  the  Planets  —  The  Elements  of 
their  Orbits  —  Determination  of  Periods  and  Distances  — 
Perturbations,  Stability  of  the  System  —  Data  referring  to 
the  Planets  themselves  —  Determination  of  Diameter,  Mass, 
Rotation,  Surface  Peculiarities,  Atmosphere,  etc. — Herschel's 
Illustration  of  the  Scale  of  the  System  —  Exercises  .  .  .  311-345 

CHAPTER  XIII.  —  THE  TERRESTRIAL  AND  MINOR  PLANETS 

—  Mercury,    Venus,    and    Mars  —  The    Asteroids  —  Intra- 
mercurial  Planets  —  Zodiacal  Light 346-381 

CHAPTER  XIV.  — THE  MAJOR  PLANETS  — Jupiter  :  its  Sat- 
ellite System;  the  Equation  of  Light,  and  the  Distance  of 
the  Sun  —  Saturn  :  its  Rings  and  Satellites  —  Uranus  :  its 
Discovery,  Peculiarities,  and  Satellites  —  Neptune :  its  Dis- 
covery, Peculiarities,  and  Satellite  —  Exercises 382-408 


TABLE   OF   CONTENTS  vii 

PAGES 

CHAPTER  XV METHODS  OF  DETERMINING  THE  PARAL- 
LAX AND  DISTANCE  OF  THE  SUN  —  Importance  and  Diffi- 
culty of  the  Problem  —  Historical — Classification  of  Methods 

—  Geometrical  Methods  —  Oppositions  of  Mars  and  certain 
Asteroids,  and  Transits  of  Venus  —  Gravitational  Methods  .  409-421 

CHAPTER  XVI.  —  COMETS  —  Their  Number,  Designation, 
and  Orbits — Their  Constituent  Parts  and  Appearance  — 
Their  Spectra  —  Physical  Constitution  and  Behavior  — 
Danger  from  Comets  —  Exercises 422-454 

CHAPTER  XVII. — METEORS  AND  SHOOTING-STARS  —  Aero- 
lites :  their  Fall  and  Physical  Characteristics ;  Cause  of 
Light  and  Heat ;  Probable  Origin  —  Shooting-Stars  :  their 
Number,  Velocity,  and  Length  of  Path  —  Meteoric  Showers : 
the  Radiant ;  Connection  between  Comets  and  Meteors  — 
Exercises 455-476 

CHAPTER  XVIII.  —  THE  STARS  — Their  Nature,  Number,  and 
Designation  —  Star-Catalogues  and  Charts  —  The  Photo- 
graphic Campaigns — Proper  Motions,  Radial  Motions,  and 
the  Motion  of  the  Sun  in  Space  —  Stellar  Parallax — Exercises  477-505 

CHAPTER  XIX.  — THE  LIGHT  OF  THE  STARS  —  Magnitudes 
and  Brightness  —  Color  and  Heat  —  Spectra  —  Variable 
Stars  —  Exercises .  .  .  506-536 

CHAPTER  XX STELLAR  SYSTEMS,  CLUSTERS,  AND  NEBULA 

—  Double  and  Multiple   Stars  —  Binaries  —  Spectroscopic 
Binaries  —  Clusters  —  Nebulse  —  The  Stellar   Universe  — 
Cosmogony  —  Exercises 537-573 

APPENDIX.  —  Transformation  of  Astronomical  Coordinates  — 
Projection  and  Calculation  of  a  Lunar  Eclipse  —  Greek 
Alphabet  and  Miscellaneous  Symbols  —  Dimensions  of  the 
Terrestrial  Spheroid  —  Time  Constants  and  other  Astro- 
nomical Constants 574-582 

TABLE  I.         Principal  Elements  of  the  Solar  System      .     .  583 

TABLE  II.        The  Satellites  of  the  Solar  System     ....  584-585 
TABLE  III.      Comets  of  which  Returns  have  been  observed  586 

TABLE  IV.       Stellar  Parallaxes,  Distances,  and  Motions       .  587 

TABLE  V.         Radial  Velocities  of  Stars 588 

TABLE  VI.      Variable  Stars 589 

TABLE  VII.     Orbits  of  Binary  Stars 590 

TABLE  VIII.  Mean  Refraction 591 

INDEX     ...  ,  592-611 


ADDENDA  TO  MANUAL   OF  ASTRONOMY 

Addendum  A.  SEC.  54. — In  the  instrument  described  in  this  section  there 
is  a  considerable  loss  of  light  from  the  two  reflections.  A  much  simpler 
form  with  only  one  reflection,  and  with  most  of  the  advantages  of  the 
Coude,  is  now  in  use  at  Cambridge  (England)  for  celestial  photography. 
But  it  commands  only  the  region  between  Declinations  +  75°  and  —  30°. 

Addendum  B.  SEC.  415.  —  Mr.  Lowell  has  recently  published  an  elabo- 
rate mathematical  investigation  of  the  temperature  of  Mars,  with  the  fol- 
lowing results :  mean  temperature  of  the  planet,  48°  F. ;  boiling  point  of 
water,  111°  F.;  density  of  air  at  the  planet's  surface,  T\  of  earth's,  corre- 
sponding to  a  barometric  height  of  2J  inches.  The  mean  temperature  ot 
the  earth  is  usually  taken  as  60°  F. 

An  expedition  sent  by  him  to  northern  Chili  in  charge  of  Professor 
Todd  is  reported  to  have  obtained  photographs  of  the  planet  showing 
many  of  the  canals,  and  some  of  them  double. 

Addendum  C.  SECS.  418-421.  —  The  present  rate  of  asteroid  discovery 
makes  it  impossible  to  keep  up  with  it  in  a  text-book.  In  1906  more  than 
100  were  found,  and  each  succeeding  year  has  added  a  large  number  to 
the  list.  Most  of  them  are  so  faint  as  to  be  observable  only  by  photog- 
raphy. Rev.  J.H.Metcalf  of  Taunton,  Massachusetts,  has  lately  made  a  very 
effective  modification  of  the  Heidelberg  method.  While  the  telescope  fol- 
lows the  .stars  by  its  driving-clock,  the  photographic  plate  receives  a  slight 
sliding  motion,  the  same  as  that  of  an  average  asteroid  in  the  region  under 
observation.  The  image  of  a  planet,  if  one  happens  to  be  present,  remains 
therefore  stationary  on  the  plate,  or  nearly  so,  during  the  entire  exposure, 
arid  is  many  times  more  intense  than  if  it  had  been  allowed  to  trail.  The 
stars  do  the  trailing,  and  are  easily  recognized  as  such. 

When  first  announced  each  new  object  is  designated  provisionally  by 
two  letters  in  an  alphabetical  arrangement :  thus  Eros  was  for  a  time 
known  as  «  DQ,"  and  already  « 1907  ZZ  "  has  been  discovered.  It  is  pro- 
posed to  continue  the  same  system,  always,  however,  prefixing  the  year. 
When  sufficient  observations  have  been  obtained  to  determine  the  planet's 
orbit,  and  its  non-identity  with  any  previously  known,  the  Director  of 
the  Recheninstitut  at  Berlin  assigns  a  permanent  "number,"  and  the 


ADDENDA   TO  MANUAL  OF  ASTRONOMY 

discoverer,  if  he  chooses,  gives  it  a  name.  Tn  August,  1911,  714  asteroids 
had  thus  received  "  numbers,"  though  many  remained  unnamed. 

Among  the  recently  discovered  planets,  TG  (588),  1906  VY,  and  1907 
XM  (all  discovered  at  Heidelberg)  are  of  special  interest.  They  form  a 
class  by  themselves,  their  orbits  not  differing  greatly  from  that  of  Jupiter 
in  size  and  period.  They  have  already  received  the  names  of  Achilles, 
Patroclus,  and  Hector.  Their  exact  orbits  are  still  only  roughly  deter- 
mined, but  it  is  clear  that  the  problem  of  their  motion  is  peculiarly  inter- 
esting, since  they  appear  to  present  approximately  the  special  case  long 
ago  pointed  out  by  Lagrange,  of  a  planet  keeping  permanently  equidistant 
from  the  sun  and  Jupiter.  1908  CS,  Nestor,  belongs  also  to  this  group. 

The  asteroid  Occlo  (475),  discovered  in  1901,  has  an  eccentricity  of 
0.38,  even  greater  than  that  of  ^thra.  Planet  1906  WD  has  the  enor- 
mous inclination  of  48°. 

Addendum  D.  SEC.  543.  —  Our  determinations  of  the  "Solar  Apex"  all 
depend  on  the  assumption  that  the  stars  whose  motions  form  the  basis  of 
the  calculation  are  moving  indiscriminately  in  all  directions,  so  that  in  the 
general  sum  the  motions  balance.  If  this  is  not  the  case,  —  i.e.,  if  there 
is  any  predominant  drift,  —  the  computed  position  of  the  Apex  will  be 
affected;  and  as  this  exact  balance  seldom  holds  good,  different  sets  of 
stars  generally  give  somewhat  different  results. 

The  recent  investigations  of  Kapteyn  on  what  he  calls  "star  streaming  " 
have  excited  great  interest  among  astronomers.  They  seem  to  show  that 
extensive  systematic  drifts  actually  exist,  and  that  the  nearer  stars  (those 
which  have  a  measurable  proper  motion)  mainly  belong  to  two  great 
systems, —  one,  the  more  numerous,  drifting  towards  the  region  of  Orion, 
the  other  streaming  in  the  opposite  direction. 


MANUAL   OF    ASTEONOMY 


INTRODUCTION 

1.    Astronomy  is  the  science  which  treats  of  the  heavenly 
bodies,  as  is  indicated  by  the  derivation  of  its  name  (aarpov  VQIJLOS). 
It  considers : 

(1)  Their  motions,  both  real  and  apparent,  and  the  laws  which 
govern  those  motions. 

(2)  Their  forms,  dimensions,  and  masses. 

(3)  Their  nature,  constitution,  and  physical  condition. 

(4)  The  effects  which  they  produce  upon  each  other  by  their 
attractions,  radiations,  or  any  other  ascertainable  influence. 

The  earth  is  an  immense  ball,  about  8000  miles  in  diameter, 
composed  of  rock  and  water,  and  covered  with  a  thin  envelope 
of  air  and  cloud.  Whirling  on  its  axis,  it  rushes  through 
empty  space  with  a  speed  fifty  times  as  great  as  that  of  the 
swiftest  shot.  On  its  surface  we  are  wholly  unconscious  of 
the  motion,  because  of  its  perfect  steadiness. 

As  we  look  up  at  night  we  see  in  all  directions  the  countless  The  off-look 
stars ;  and  conspicuous  among  them,  and  looking   like    stars,  from  the 
though  very  different  in  their  real  nature,  are  scattered  a  few 
planets.     Here  and  there  appear  faintly  shining  clouds  of  light, 
like  the  so-called  Milky  Way  and  the  nebulse,  and  perhaps  now 
and  then  a  comet.     Most  striking  of  all,  if  she  happens  to  be 
in  the  heavens  at  the  time,  though  really  the  most  insignificant 
of  all,  is  the  moon.     By  day  the  sun  alone  is  visible,  flooding 
the  air  with  its  light  and  hiding  the  other  bodies  from  the 
unaided  eye,  but  not  all  of  them  from  the  telescope. 

i 


MANUAL   OF   ASTRONOMY 


Branches  of 
astronomy. 


2.  The  Heavenly  Bodies.  —  The   bodies  thus  seen  from  the 
earth  are  the  heavenly  bodies.     For  the  most  part  they  are  globes 
like    the   earth,  whirling    on  their  axes,  and  moving  swiftly, 
though  at  such  distances  from   us  that  their  motions  can  be 
detected  only  by  careful  observation. 

They  may  be  classified  as  follows:  First,  the  solar  system 
proper,  composed  of  the  sun,  the  planets  which  revolve  around 
it,  and  the  satellites  which  attend  the  planets  in  their  motion. 
The  moon  thus  accompanies  the  earth.  The  distances  between 
these  bodies  are  enormous  as  compared  with  the  size  of  the 
earth;  and  the  sun,  which  rules  them  all,  is  a  body  of  almost 
inconceivable  magnitude. 

Secondly,  we  have  the  comets  and  the  meteors,  which,  while 
they  acknowledge  the  sun's  dominion,  move  in  orbits  of  a  dif- 
ferent shape  and  are  bodies  of  a  very  different  character. 

Thirdly,  we  have  the  stars,  at  distances  from  us  immensely 
greater  than  even  those  which  separate  the  planets.  The 
visible  stars  are  suns,  bodies  like  our  own  sun  in  nature,  and  like 
it,  self-luminous,  while  the  planets  and  their  satellites  shine  only 
by  reflected  sunlight.  The  telescope  reveals  millions  of  stars 
invisible  to  the  naked  eye,  and  there  are  others,  possibly  thou- 
sands of  them,  that  are  dark  and  do  not  shine,  but  manifest 
their  existence  by  effects  upon  their  neighbors. 

Finally,  there  are  the  nebulce,  of  which  we  know  very  little 
except  that  they  are  cloudlike  masses  of  shining  matter,  and 
belong  to  the  region  of  the  stars. 

3,  Branches   of    Astronomy.  —  Astronomy    is    divided    into 
many  branches,  some  of  which  generally  recognized  are   the 
following : 

(1)  Descriptive   Astronomy,      This,   as   its   name   implies,   is 
merely  an  orderly  statement  of  astronomical  facts  and  principles. 

(2)  Spherical  Astronomy.     This,  discarding  all  considerations 
of  absolute  dimensions  and  distances,  treats  the  heavenly  bodies 
simply  as  objects  on  the  surface  of  the  celestial  sphere  ;  it  deals 


INTRODUCTION  3 

only   with   angles    and    directions,    and,    strictly   regarded,   is 
merely  spherical  trigonometry  applied  to  astronomy. 

(3)  Practical  Astronomy.     This  treats   of   the   instruments, 
the  methods  of  observation,  and  the  processes  of  calculation  by 
which  astronomical  facts  are  ascertained.     It  is  quite  as  much 
an  art  as  a  science. 

(4)  Theoretical  Astronomy.     This  deals  with  the  calculation 
of  orbits  and  ephemerides,  including  the  effect  of  perturbations. 

(5)  Astronomical  Mechanics.     This  is  simply  the  application 
of  mechanical  principles  to  explain  astronomical  facts,  chiefly  the 
planetary  and  lunar  motions.     It  is  sometimes  called  "  gravita- 
tional astronomy,"   because,   with  few  exceptions,   gravitation 
is   the   only  force   sensibly   concerned  in  the   motions   of  the 
heavenly  bodies. 

Until  about  1860  this  branch  of  the  science  was  generally  Abandon- 
designated  "  physical  astronomy,"  but  the  term  is  now  objection-  ^n*  ^ 
able  because  of  late  it  has  been  used  by  some  writers  to  denote  a  "  physical 
very  different  and  comparatively  new  branch  of  the  science,  viz. :  astron>- 

(6)  Astronomical  Physics,  or  Astro-Physics.     This  treats  of 
the  physical  characteristics  of  the  heavenly  bodies,  their  bright- 
ness and  spectroscopic  peculiarities,  their  temperature  and  radi- 
ation, the  nature  and  condition  of  their  atmospheres  and  surfaces, 
and  all  phenomena  which  indicate  or  depend  on  their  physical 
condition.     It  is  sometimes  called  The  New  Astronomy. 

The  above  branches  are  not  distinct  and  separate,  but  overlap  in  all 
directions.  Valuable  works  exist,  however,  bearing  the  different  titles 
indicated  above,  and  it  is  important  for  the  student  to  know  what  subjects 
he  may  expect  to  find  discussed  in  each,  although  they  do  not  distribute 
the  science  between  them  in  any  strictly  logical  and  mutually  exclusive 
manner. 

4.  Rank  of  Astronomy  among  the  Sciences.  —  Astronomy  is 
the  oldest  of  the  natural  sciences.  Obviously,  in  the  very 
infancy  of  the  race  the  rising  and  setting  of  the  sun,  the 
phases  of  the  moon,  and  the  progress  of  the  seasons  must  have 


MANUAL   OF   ASTRONOMY 


Astronomy 
still  pro- 
gressive. 


Use  in  navi- 
gation and 
geodesy. 


Use  in  regu- 
lation of 
time. 


Chief  value 
purely  intel- 
lectual. 


compelled  the  attention  of  even  the  most  unobservant.  Nearly 
the  earliest  of  all  existing  records  relate  to  astronomical  subjects, 
such  as  eclipses  and  the  positions  of  the  planets. 

As  astronomy  is  the  oldest  of  the  sciences,  so  also  it  is  one 
of  the  most  perfect  and  complete,  though  not  in  the  sense  that 
it  has  reached  a  maturity  which  admits  no  further  development, 
for  in  fact  it  was  never  more  vigorously  alive  or  growing  faster 
than  at  present.  In  certain  aspects  astronomy  is  also  the 
noblest  of  the  sisterhood,  being  the  most  "  unselfish  "  of  them 
all,  cultivated  not  so  much  for  material  profit  as  for  pure  love 
of  learning. 

5.  Utility.  —  But  although  bearing  less  directly  upon  the 
material  interests  of  life  than  the  more  modern  sciences  of 
physics  and  chemistry,  it  is  really  of  high  utility. 

It  is  by  means  of  astronomy  that  the  latitude  and  longitude 
of  points  upon  the  earth's  surface  are  determined,  and  by  such 
determinations  alone  is  it  possible  to  conduct  extensive  naviga- 
tion. Moreover,  all  the  operations  of  surveying  upon  a  large 
scale,  such  as  the  determination  of  international  boundaries, 
depend  more  or  less  upon  astronomical  observations. 

The  same  is  true  of  all  operations  which,  like  the  railway 
service,  require  an  accurate  knowledge  and  observance  of  the 
time ;  for  our  fundamental  timekeeper  is  the  daily  revolu- 
tion of  the  heavens,  as  determined  by  the  astronomer's  transit 
instrument. 

At  present,  however,  the  end  and  object  of  astronomical 
study  is  chiefly  knowledge,  pure  and  simple.  It  is  not  likely 
that  great  inventions  and  new  arts  will  grow  out  of  its  prin- 
ciples, such  as  are  continually  arising  from  chemical,  physical, 
and  biological  studies ;  but  it  would  be  rash  to  say  that  such 
outgrowths  are  impossible. 

The  student  of  astronomy  must,  therefore,  expect  his  chief 
profit  to  be  intellectual,  —  in  the  widening  of  the  range  of 
thought  and  conception,  in  the  pleasure  attending  the  discovery 


INTRODUCTION  5 

of  simple  law  working  out  the  most  far-reaching  results,  in  the 
delight  over  the  beauty  and  order  revealed  by  the  telescope 
and  spectroscope  in  systems  otherwise  invisible,  in  the  recogni- 
tion of  the  essential  unity  of  the  material  universe  and  of  the 
kinship  between  his  own  mind  and  the  Infinite  Reason. 

In  ancient  time  it  was  believed  that  human  affairs  of  every  kind,  the 
welfare  of  nations,  and  the  life  history  of  individuals,  were  controlled,  or 
at  least  prefigured,  by  the  motions  of  the  stars  and  planets ;  so  that  from 
the  study  of  the  heavens  it  ought  to  be  possible  to  predict  futurity.     The 
pseudo-science  of  astrology,  based  upon  this  belief,  supplied  the  motives  that   Astrology 
led  to  most  of  the  astronomical  observations  of  the  ancients.     As  modern   a  pseudo- 
chemistry  had  its  origin  in  alchemy,  so  astrology  was  the  progenitor  of 
astronomy,  and  it  is  remarkable  how  persistent  a  hold  this  baseless  delusion 
still  retains  upon  the  credulous. 

6.    Place  in  Education. — Apart  from  the  utility  of  astronomy 
in  the  ordinary  sense  of  the  word,  the  study  of  the  science  is  of 
high  value  as  an  intellectual  training.     No  other  so  operates  Educational 
to  give  us,  on  the  one  hand,  just  views  of  our  real  insignificance  value- 
in  the  universe  of  space,  matter,  and  time,  or  to  teach  us,  on 
the  other  hand,  the  dignity  of  the  human  intellect  as  being  the 
offspring,  and  measurably  the  counterpart,  of  the  Divine,  —  able 
in  a  sense  to  comprehend  the  universe  and  understand  its  plan 
and  meaning. 

The  study  of  the  science  cultivates  nearly  every  faculty  of 
the  mind ;  the  memory,  the  reasoning  power,  and  the  imagina- 
tion all  receive  from  it  special  exercise  and  development.  By 
the  precise  and  mathematical  character  of  many  of  its  discussions 
it  enforces  exactness  of  thought  and  expression,  and  corrects 
the  vague  indefiniteness  which  is  apt  to  be  the  result  of  purely 
literary  training ;  while,  on  the  other  hand,  by  the  beauty  and 
grandeur  of  the  subjects  which  it  presents,  it  stimulates  the 
imagination  and  gratifies  the  poetic  sense. 

NOTE.  —  The  occasional  references  to  "Physics"  refer  to  Gage's  Principles  of 
Physics  (Goodspeed's  revision). 


CHAPTER  I 
PRELIMINARY  CONSIDERATIONS  AND   DEFINITIONS 

Fundamental  Notions  and  Definitions— Astronomical  Coordinates  and  the  "Doctrine 
of  the  Sphere  "  —  The  Celestial  Globe 

ASTRONOMY,  like  all  the  other  sciences,  has  a  terminology  of 
its  own,  and  uses  technical  terms  in  the  description  of  its  facts 
and  phenomena.  In  a  popular  work  it  would  be  proper  to 
avoid  such  terms  as  far  as  possible,  even  at  the  expense  of 
circumlocutions  and  occasional  ambiguity;  but  in  a  text-book  it 
is  desirable  that  the  student  should  be  introduced  to  the  most 
important  of  them  at  the  very  outset  and  be  made  sufficiently 
familiar  with  them  to  use  them  intelligently  and  accurately . 

7.    The  Celestial  Sphere.1  —  The   sky  appears  like  a  hollow 
vault,  to  which  the  stars  seem  to  be  attached,  like  gilded  nail- 
heads  upon  the  inner  surface  of  a  dome.     We   cannot  judge 
of  the  distance  to  this   surface  from  the  eye  further  than  to 
perceive  that  it  must  be  very  far  away ;  it  is  therefore  natural 
and  extremely  convenient  to  regard  the  distance   of  the  sky 
The  celestial  as  everywhere  the  same  and  unlimited.     The  celestial  sphere, 
sphere  ag  ^  jg  ca}ie(j   is  conceived  of  as  so  enormous  that  the  whole 

conceived 

as  infinite,  material  universe  of  stars  and  planets  lies  in  its  center  like  a 
few  grains  of  sand  in  the  middle  of  the  dome  of  the  Capitol. 
Its  diameter,  in  technical  language,  is  taken  as  mathematically 
infinite,  i.e.,  greater  than  any  assignable  quantity. 

Since  the  radius  of  the  sphere  is  thus  infinite,  it  follows  that 
all  the  lines  of  any  set  of  parallels  will  appear,  if  produced 

1  The  study  of  the  celestial  sphere  and  its  circles  is  greatly  aided  by  the  use 
of  a  globe  or  armillary  sphere.  Without  some  such  apparatus  it  is  rather  difficult 
for  a  beginner  to  get  clear  ideas  upon  the  subject. 

6 


PRELIMINARY  CONSIDERATIONS   AND  DEFINITIONS      7 


indefinitely,  to  pierce  it  at  a  single  point,  the  vanishing  point 
of  perspective,  or  the  point  at  infinity  of  projective  geometry. 
However  far  apart  the  lines  may  be  and  whatever,  therefore, 
may  be  the  distances  in  miles  between  the  points  at  which  they 
pierce  the  surface  of  the  celestial  sphere,  yet,  seen  by  the 
observer  at  its  infinitely  distant  center,  the  angular  distance 
between  those  points  is  utterly  insensible,  and  they  coalesce 
into  one.  Thus  the  axis  of  the  earth  and  all  lines  parallel  to 
it  pierce  the  heavens  at  one  point,  the  celestial  pole;  and  the 
plane  of  the  earth's  equator,  keep- 
ing parallel  to  itself  during  her 
annual  circuit  around  the  sun, 
marks  out  only  one  celestial  equa- 
tor in  the  sky. 

8.  The  place  of  a  heavenly  body 
is  simply  the  point  where  a  line 
drawn  from  the  observer  through 
the  body  in  question  and  continued 
onward  pierces  the  celestial  sphere. 
It  depends  solely  upon  the  direc- 
tion of  the  body  and  has  nothing 

to  do  with  its  distance.  Thus,  in  Fig.  1  A,  B,  C,  etc.,  are  the 
apparent  places  of  a,  b,  c,  etc.,  the  observer  being  at  0.  Objects 
that  are  nearly  in  line  with  each  other,  as  h,  i,  Jc,  will  appear 
close  together  in  the  sky,  however  great  the  real  distance  between 
them.  The  moon,  for  instance,  often  looks  to  us  very  near  a 
star,  which  is  always  at  an  immeasurable  distance  beyond  her. 

9.  Linear  and  Angular  Dimensions  and  Measurement.  —  Linear 
dimensions  are  such  as  can  be  expressed  in  linear  units;  i.e., 
in  miles,  feet,  or  inches ;    kilometers,  meters,  or  millimeters. 
Angular  dimensions  are  expressed  in  angular  units ;  i.e.,  in  degrees, 
minutes,  and  seconds,  or  sometimes  in  radians,  the  radian  being 
the  angle  which  is  measured  by  an  arc  equal  in  length  to  the 
radius,  determined  by  dividing  the  circumference  by  2  TT. 


Apparent 
convergence 
of  parallels 
to  a  single 
point  on  the 
celestial 
sphere. 


FIG.  1 


Place  of  a 
heavenly 
body  de- 
pends solely 
on  its  direc- 
tion from 
observer. 


Value  of  the 
radian  in 


minutes, 
and  seconds. 


MANUAL   OF   ASTRONOMY 


Angular 
units  used 


ments  on 

celestial 

sphere. 


The  radian,  therefore,  equals  57°.29  (i.e.,  360°  H-  2  TT), 
or  3437'.75  (i.e.,  21600'  -f-  2  TT), 
or  206264".8  (i.e.,  1  296000"  -*-  27r). 

Hence,  to  reduce  to  seconds  of  arc  an  angle  expressed  in  radians, 
we  must  multiply  its  value  in  radians  by  206264-8  ;  a  relation  of 
which  we  shall  make  frequent  use. 

Obviously,  angular  units  alone  can  properly  be  used  in  describ- 
ing apparent  distances  in  the  sky.  One  cannot  say  correctly 
ing  measure-  that  the  two  stars  known  as  "-the  pointers"  are  so  many  feet 
apart ;  their  distance  is  about  five  degrees. 

It  is  very  important  that  the  student  of  astronomy  should 
accustom  himself  as  soon  as  possible  to  estimate  celestial  meas- 
ures in  angular  units.  A  little  practice  soon  makes  it  easy, 
although  the  beginner  is  apt  to  be  embarrassed  by  the  fact  that 
the  sky  appears  to  the  eye  to  be  not  a  true  hemisphere,  but  a 
flattened  vault,  so  that  all  estimates  of  angular  distances  for 
objects  near  the  horizon  are  apt  to  be  exaggerated.  The  moon 
when  rising  or  setting  looks  to  most  persons  much  larger  than 
when  overhead,  and  the  "  Dipper-bowl "  when  underneath  the 
pole  seems  to  cover  a  much  larger  area  than  when  above  it. 

Apparent  This  illusion  (for  it  is  merely  an  illusion),  which  makes  the  sun  and 

enlargement  heavenly  bodies  when  near  the  horizon  appear  larger  than  when  high  up 

of  sun  and      jn  ^Q  gj^  |g  prokakiy  due  to  the  fact  that  in  the  latter  case  we  have  no 

the  horizon     intervening  objects  by  which  to  estimate  the  distance,  and  it  therefore  is 

judged  to  be  smaller  than  at  the  horizon.     If  we  look  at  the  sun  or  moon 

when  near  the  horizon  through  a  lightly  smoked  glass  which  cuts  off  the 

view  of  the  landscape,  the  object  immediately  shrinks  to  its  ordinary  size. 


Relation 
between 
distance, 
radius,  and 
angular 
semi- 
diameter  of 
a  globe. 


10.  Relation  between  the  Distance  and  Apparent  Size  of  an 
Object.  —  Suppose  a  globe  having  a  (linear)  radius  BC  equal  to 
r.  As  seen  from  the  point  A  (Fig.  2)  its  apparent  (i.e.,  angular) 
semidiameter  will  be  BAC  or  s,  its  distance  being  AC  or  R. 

We  have  immediately,  from  trigonometry,  since  B  is  a  right 
angle,  sin  s  =  r  /R,  whence  also  r  =  R  X  ?in  s,  and  R  =  r  •*-  sin  s. 


PRELIMINARY  CONSIDERATIONS  AND  DEFINITIONS       9 

If,  as  is  usual  in  astronomy,  the  diameter  of  an  object  is 
small  as  compared  with  its  distance,  so  that  sin  s  practically 


FIG.  2 

equals  s  itself,  we  may  write  s  =  r/R,  which  gives  s  in  radians 
(not  in  degrees  or  seconds).  If  we  wish  to  have  it  in  the 
ordinary  angular  units, 

8°  =  57.3r/^;  or  «'  =  3437.7  r/JR;  or  s"  =  206264.8  r/R} 
also  R  =  206264.8  r/«";    andr  =  ^«"/206264.8; 

where  s°  means  s  in  degrees  ;  s',  in  minutes  of  arc ;  s",  in  seconds 
of  arc. 

In  either  form  of  the  equation  we  see  that  the  apparent 
diameter  varies  directly  as  the  linear  diameter  and  inversely  as 
the  distance. 

In  the  case  of  the  moon,  R  =  about  239000  miles ;  and  r, 
1081  miles.  Hence  s  (in  radians)  =  ^tf-o"o  =  jj-y  °f  a  radian, 
which  is  about  933",  —  a  little  more  than  one  fourth  of  a 
degree. 

It  may  be  mentioned  here  as  a  rather  curious  fact  that  to  most  persons   Apparent 
the  moon,  when  at  a  considerable  altitude,  appears  about  a  foot  in  diam-  distance  of 
eter ;  —  at  least,  this  seems  to  be  the  average  estimate.     This  implies  that  *~e  surface 
the  surface  of  the  sky  appears  to  them  only  about  110  feet  away,  since  tial  spnere 
that  is  the  distance  at  which  a  disk  one  foot  in  diameter  would  have  an 
angular  diameter  of  Tyff  of  a  radian,  or  £°. 

Probably  this  is  connected  with  the  physiological  fact  that  our  muscular 
sense  enables  us  to  judge  moderate  distances  pretty  fairly  up  to  80  or  100 
feet,  through  the  "binocular  parallax"  or  convergence  of  the  eyes  upon 
the  object  looked  at.  Beyond  that  distance  the  convergence  is  too  slight 
to  be  perceived.  It  would  seem  that  we  instinctively  estimate  the  moon's 
distance  as  small  as  our  senses  will  permit  when  there  are  no  intervening 
objects  which  compel  our  judgment  to  put  her  further  off. 


10 


MANUAL   OF   ASTRONOMY 


POINTS   AND  CIRCLES   OF   EEFERENCE   AND  SYSTEMS 
OF  COORDINATES 

In  order  to  be  able  to  describe  intelligently  the  position  of  a 
heavenly  body  in  the  sky,  it  is  convenient  to  suppose  the  inner 
surface  of  the  celestial  sphere  to  be  marked  off  by  circles  traced 
upon  it,  —  imaginary  circles,  of  course,  like  the  meridians  and 
parallels  of  latitude  upon  the  surface  of  the  earth. 

Three  distinct  systems  of  such  circles  are  made  use  of  in 
astronomy,  each  of  which  has  its  own  peculiar  adaptation  for  its 
special  purposes. 


A.    SYSTEM  DEPENDING  ON  THE  DIRECTION  OF  GRAVITY  AT 
THE   POINT   WHERE   THE    OBSERVER   STANDS 

11.  The  Zenith  and  Nadir.  —  If  we  suspend  a  plumb-line,  and 
imagine  the  line  extended  upward  to  the  sky,  it  will  pierce 
the  celestial  sphere  at  a  point  directly  overhead,  known  as  the 
Astronomical  Zenith,  or  the  Zenith  simply,  unless  some  other 
qualifier  is  annexed. 

As  will  be  seen  later  (Sec.  130,  b),  the  plumb-line  does  not 
point  exactly  to  the  center  of  the  earth,  because  the  earth 
rotates  on  its  axis  and  is  not  strictly  spherical.  If  an  imagi- 
nary line  be  drawn  from  the  center  of  the  earth  upward 
through  the  observer,  and  produced  to  the  celestial  sphere, 
it  marks  a  different  point,  known  as  the  geocentric  zenith, 
which  is  never  very  far  from  the  astronomical  zenith,  but 
must  not  be  confounded  with  it. 

For  most  purposes  the  astronomical  zenith  is  the  better 
practical  point  of  reference,  because  its  position  can  be  deter- 
mined directly  by  observation,  which  is  not  the  case  with  the 
other. 


PRELIMINARY  CONSIDERATIONS  AND  DEFINITIONS     11 

The  Nadir  is  the  point  opposite  to  the  zenith,  directly  under 
foot  in  the  invisible  part  of  the  celestial  sphere. 

Both  "  zenith  "  and  "  nadir  "  are  derived  from  the  Arabic,  as  are  many 
other  astronomical  terms.  It  is  a  reminiscence  of  the  centuries  when  the 
Arabs  were  the  chief  cultivators  of  science. 

12.  The  Horizon.  —  If  now  we  imagine  a  great  circle  drawn  The  horizon 
completely  around  the  celestial  sphere  half-way  between  the  defined< 
zenith  and  nadir,  and  therefore  90°  from  each  of  them,  it  will 

be  the  Horizon  (pronounced  ho-ri'-zon,  not  hor'-i-zon). 

Since  the  surface  of  still  water  is  always  perpendicular  to 
the  direction  of  gravity,  we  may  also  define  the  horizon  as  the 
great  circle  in  which  a  plane  tangent  to  a  surface  of  still  water 
at  the  place  of  observation  cuts  the  celestial  sphere. 

Many  writers  distinguish  between  the  sensible  and  rational  Unneces- 
horizons,  —  the  former  being  denned  by  a  horizontal  plane  drawn  sary  distinc- 

tion  foptwppn 

through  the  observer's  eye,  while  the  latter  is  defined  by  a  plane  sensible  and 
parallel  to  this,  but  drawn  through  the  center  of  the  earth,  rational 
These  two  planes,  however,  though  4000  miles  apart,  coalesce 
upon  the  infinite  celestial  sphere  into  a  single  great  circle  90° 
from  both  zenith  and  nadir,  agreeing  with  the  first  definition 
given  above.     The  distinction  is  unnecessary. 

13.  Visible  Horizon. — The  word  "  horizon  "  (from  the  Greek)  The  visible 
means  literally  "the  boundary"  —  that  is,  the  limit  of  the  land-  horizon- 
scape,  where  sky  meets  earth  or  sea;  and  this  boundary  line 

is  known  in  astronomy  as  the  visible  horizon.  On  land  it  is 
of  no  astronomical  importance,  being  irregular;  but  at  sea  it 
is  practically  a  true  circle,  nearly  coinciding  with  the  horizon 
above  defined,  but  a  little  below  it.  When  the  observer's  eye 
is  at  the  water-level,  the  coincidence  is  exact ;  but  if  he  is 
at  an  elevation  above  the  surface,  the  line  of  sight  drawn 
from  his  eye  tangent  to  the  water  inclines  or  dips  down,  on 
account  of  the  curvature  of  the  earth,  by  a  small  angle  known 
as  the  dip  of  the  horizon,  to  be  discussed  further  on  (Sec.  77). 


12 


MANUAL   OF   ASTRONOMY 


14.  Vertical  Circles ;  the  Meridian  and  the  Prime  Vertical.  - 
Vertical  circles  are  great  circles  drawn  from  the  zenith  at  right 
angles  to  the  horizon,  and  therefore  passing  through  the  nadir 
also.     Their  number  is  indefinite. 

That  particular  vertical  circle  which  passes  north  and  south 
through  the  pole,  to  be  defined  hereafter,  is  known  as  the  Celes- 
tial Meridian,  and  is  evidently  the  circle  traced  upon  the  celestial 
sphere  by  the  plane  of  the  terrestrial  meridian  upon  which  the 
observer  is  located.  The  vertical  circle  at  right  angles  to 
the  meridian  is  called  the  Prime  Vertical.  The  points  where 


FIG.  3.  — The  Horizon  and  Vertical  Circles 


0,  the  place  of  the  observer. 
OZ,  the  observer's  vertical. 
Z,  the  zenith  ;  P,  the  pole. 
SWNE,  the  horizon. 
SZPN,  the  meridian. 
EZW,  the  prime  vertical. 


M,  some  star. 

ZMH,  arc  of  the  star's  vertical  circle. 

TMR,  the  star's  almucantar. 

Angle  TZM,  or  arc  SH,  star's  azimuth. 

Arc  HM,  star's  altitude. 

Arc  ZM,  star's  zenith-distance. 


the  meridian  intersects  the  horizon  are  the  north  and  south 
points;  and  the  east  and  west  points  are  midway  between  them. 
These  are  known  as  the  Cardinal  Points. 

The  parallels  of  altitude,  or  almucantars,  are  small  circles  of 
the  celestial  sphere  drawn  parallel  to  the  horizon,  sometimes 
called  circles  of  equal  altitude. 

15.  Altitude  and  Zenith-Distance.  —  The  Altitude  of  a  heav- 
enly body  is  its  angular  elevation  above  the  horizon,  i.e., 
the  number  of  degrees  between  it  and  the  horizon,  measured 
on  a  vertical  circle  passing  through  the  object.  In  Fig.  3  the 


PRELIMINARY  CONSIDERATIONS  AND  DEFINITIONS     13 

vertical  circle  ZMH  passes  through  the  body  M.  The  arc  MH 
is  the  altitude  of  M,  and  the  arc  ZM  (the  complement  of  MH) 
is  its  zenith-distance. 

16.  Azimuth. — The  Azimuth  (an  Arabic  word)  of  a  heavenly  Azimuth 
body  is  the  same  as  its   "bearing"   in  surveying;   measured,  defined- 
however,  from  the  true  meridian  and  not  from  the  magnetic. 

It  may  be  defined  as  the  angle  formed  at  the  zenith  between 
the  meridian  and  the  vertical  circle  which  passes  through  the 
object ;  or,  what  comes  to  the  same  thing,  it  is  the  arc  of  the 
horizon  intercepted  between  the  south  point  and  the  foot  of  this 
circle. 

In  Fig.  3  SZM  is  the  azimuth  of  M,  as  is  also  the  arc  SH, 
which  measures  this  angle.    The  distance  of  H  from  the  east  or 
west  point  of  the  horizon  is  called  the  amplitude  of  the  body,  Amplitude 
but  the  term  is  seldom   used  except  in  describing  the  point  defined- 
where  the  sun  or  moon  rises  or  sets. 

There  are  various  ways  of  reckoning  azimuth.      Formerly  Method  of 
it  was  usually  expressed  in  the  same  way  as  the  "  bearing  "  in  reckoning 
surveying;    i.e.,  so   many  degrees    east  or  west   of   north    or 
south.     In   the   figure,   the   azimuth  of   M  thus  expressed  is 
about  S.  50°  E.     The  more   usual  way  at  present,  however, 
is  to  reckon  it  from  the  south  point  clear  around  through  the 
west  to  the  point  of  beginning,  so  that  the   arc   SWNKEH 
would  be  the  azimuth  of  Jf,  —  about  310°. 

17.  Altitude    and    azimuth    are    for   many   purposes    in  con-  inconven- 
venient,  because  they  continually  change  for  a  celestial  object.  lence  of  altl" 
It  is  desirable,  therefore,  in  defining  the  place  of  a  body  in  the  azimuth, 
heavens,  to  use  a  different  way  which  shall  be  free  from  this 
objection ;  and  this  can  be  done  by  taking  as  the  fundamental 

line  of  our  system,  not  the  direction  of  gravity,  which  is  differ- 
ent at  any  two  different  points  on  the  earth's  surface  and  is 
continually  changing  as  the  earth  revolves,  but  the  direction 
of  the  earths  axis,  which  is  practically  constant. 


14 


MAKUAL   OF   ASTRONOMY 


B.    SYSTEM  DEPENDING  UPON   THE   DIRECTION  OF  THE 
EARTH'S  AXIS   OF  ROTATION 

Apparent  18.  The  Apparent  Diurnal  Rotation  of  the  Heavens.  —  If  on 

theTe'avens    some  clear  evening  in  the  early  autumn,  say  about  eight  o'clock 
on  the  22d  of  September,  we  face  the  north,  we  shall  find  the 


FIG.  4.  —  The  Northern  Circumpolar  Constellations 

appearance  of  that  part  of  the  heavens  directly  before  us  sub- 
stantially as  shown  in  Fig.  4.  In  the  north  is  the  constellation 
of  the  Great  Bear  (Ursa  Major),  characterized  by  the  conspicu- 
ous group  of  seven  stars,  known  as  the  Great  Dipper,  which 
lies  with  its  handle  sloping  upward  to  the  west.  The  two 


PRELIMINARY  CONSIDERATIONS  AND  DEFINITIONS     15 

easternmost  stars  of  the  four  which  form  its  bowl  are  called  the 
pointers,  because  they  point  to  the  pole-star,  —  a  solitary  star  The  pole- 
not  quite  half-way  from  the  horizon  to  the  zenith  (in  the  latitude  star  and  the 

J  pointers. 

of  New  York),  and  about  as  bright  as  the  brighter  of  the  two 
pointers.  It  is  often  called  Polaris. 

High  up  on  the  opposite  side  of  the  pole-star  from  the  Great 
Dipper,  and  at  nearly  the  same  distance,  is  an  irregular  zigzag 
of  five  stars,  each  about  as  bright  as  the  pole-star  itself.  This 
is  the  constellation  of 
Cassiopeia. 

If  now  we  watch  these 
stars  for  only  a  few 
hours,  we  shall  find  that 
while  all  the  configura- 
tions remain  unaltered, 
their  places  in  the  sky 
are  slowly  changing. 
The  Dipper  slides  down- 
ward towards  the  north, 
so  that  by  eleven  o'clock 
the  pointers  are  directly 
under  Polaris.  Cassio- 
peia  still  keeps  oppo- 

site,  however,  rising  towards  the  zenith;  and  if  we  were  to 
continue  to  watch  them  the  whole  night,  we  should  find  that 
all  the  stars  appear  to  be  moving  in  circles  around  a  point  near 
the  pole-star,  revolving  in  the  opposite  direction  to  the  hands 
of  a  watch  (as  we  look  up  towards  the  north),  with  a  steady 
motion  which  takes  them  completely  around  once  a  day,  or, 
to  be  exact,  once  in  the  sidereal  day,  consisting  of  23h56m48.l 
of  ordinary  time.  They  behave  just  as  if  they  were  attached 
to  the  inner  surface  of  a  huge  revolving  sphere. 

Instead  of  watching  the  stars  with  the  eye,  the  same  result 
can  be  still  better  reached  by  photography.     A  camera  is  pointed 


16 


MANUAL   OF   ASTRONOMY 


Polar  star 
trails. 


up  towards  the  pole-star  and  remains  firmly  fixed  while  the  stars, 
by  their  diurnal  motion,  impress  their  "  trails  "  upon  the  plate. 
Fig.  5  is  copied  from  a  negative  made  by  the  author  with  an 
exposure  of  about  three  hours. 

If  instead  of  looking  towards  the  north  we  now  look  south- 
ward, we  shall  find  that  there  also  the  stars  appear  to  move  in 
the  same  kind  of  way.  All  that  are  not  too  near  the  pole-star 
rise  somewhere  in  the  eastern  horizon,  ascend  not  vertically  but 
obliquely  to  the  meridian,  and  descend  obliquely  to  their  setting 
at  points  on  the  western  horizon.  The  motion  is  always  in  an 
arc  of  the  circle,  called  the  star's  diurnal  circle,  the  size  of  which 
depends  upon  the  star's  distance  from  the  pole.  Moreover,  all 
these  arcs  are  strictly  parallel. 

The  ancients  accounted  for  these  obvious  facts  by  supposing 
the  stars  actually  fixed  upon  a  real  material  sphere,  really 
turning  daily  in  the  manner  indicated.  According  to  this  view 
there  must  therefore  be  upon  the  sphere  two  opposite,  pivotal 
points  which  remain  at  rest,  and  these  are  the  poles. 

19.  Definition  of  the  Poles.  —  The  Celestial  Poles,  or  Poles  of 
Rotation  (when  it  is  necessary,  as  sometimes  happens,  to  dis- 
tinguish between  these  poles  and  the  poles  of  the  ecliptic),  may 
therefore  be  defined  as  those  two  points  in  the  sky  where  a  star 
would  have  no  diurnal  motion.  The  exact  position  of  either 
pole  may  be  determined  with  proper  instruments  by  finding  the 
center  of  the  small  diurnal  circle  described  by  some  star  near 
it,  as  for  instance  by  the  pole-star. 

Since  the  two  poles  are  diametrically  opposite  in  the  sky,  only  one  of 
them  is  usually  visible  from  a  given  place  ;  observers  north  of  the  equator 
see  only  the  north  pole,  and  vice  versa  in  the  southern  hemisphere. 

Knowing  as  we  now  do  that  the  apparent  revolution  of  the 
celestial  sphere  is  due  to  the  real  rotation  of  the  earth  on 
its  axis,  we  may  also  define  the  poles  as  the  two  points  where 
the  earths  axis  of  rotation  (or  any  set  of  lines  parallel  to  it), 
produced  indefinitely,  would  pierce  the  celestial  sphere. 


PRELIMINARY  CONSIDERATIONS  AND  DEFINITIONS     17 


20.  The  Celestial  Equator,  or  Equinoctial,  and  Hour-Circles.  — 

The  Celestial  Equator  is  the  great  circle  of  the  celestial  sphere, 
drawn  half-way  between  the  poles  (therefore  everywhere  90°  from 
each  of  them),  and  is  the  great  circle  in  which  the  plane  of  the 
earth's  equator  cuts  the  celestial  sphere  (Fig.  6).  It  is  often 
called  the  Equinoctial.  Small  circles  drawn  parallel  to  the 
equinoctial,  like  the  parallels  of  latitude  on  the  earth,  are  called 
parallels  of  declination,  a  star's 
parallel  of  declination  being  iden- 
tical with  its  diurnal  circle. 

The  great  circles  of  the  celestial 
sphere  which  pass  through  the  poles, 
like  the  meridians  on  the  earth, 
and  are  therefore  perpendicular 
to  the  celestial  equator,  are  called 
Hour-  Circles.  On  celestial  globes 
twenty-four  of  them  are  usually 
drawn,  corresponding  one  to  each 
of  the  twenty-four  hours,  but  the 
real  number  is  indefinite ;  an 
hour-circle  can  be  drawn  through 
any  star.  That  particular  hour-circle  which  at  any  moment 
passes  through  the  zenith  of  the  observer  coincides  with  the 
celestial  meridian,  already  defined. 

21.   Declination  and  Hour  Angle The  Declination  of  a  star 

is  its  distance  in  degrees  north  or  south  of  the  celestial  equator ; 
-f-  if  north,  —  if  south.  It  corresponds  precisely  with  the  lati- 
tude of  a  place  on  the  earth's  surface,  but  cannot  be  called 
celestial  latitude,  because  the  term  has  been  preoccupied  by  an 
entirely  different  quantity  to  be  defined  later  (Sec.  27). 

The  Hour  Angle  of  a  star  at  any  moment  is  the  angle  at 
the  pole  between  the  celestial  meridian  and  the  hour-circle  of  the 
star.  In  Fig.  7,  for  the  body  m  it  is  the  angle  mPZ,  or  the 
arc  QY. 


FIG.  6.  — The  Plane  of  the  Earth's 
Equator  produced  to  cut  the  Celes- 
tial Sphere 


Definition 
of  the 
celestial 
equator. 


Parallels  of 
declination 
identical 
with  diurna\ 
circles. 


Hour-circles 
defined.  The 
meridian 
as  an 
hour-circle. 


Declination 
defined. 


Hour  angle 
defined. 


18 


MANUAL   OF   ASTRONOMY 


Relation  of 
units  of 

time  to  units 

of  angle. 


This  angle,  or  arc,  may  of  course  be  measured  like  any  other, 
in  degrees,  but  since  it  depends  upon  the  time  which  has  elapsed 
since  the  body  was  last  on  the  meridian,  it  is  more  usual  to 
measure  it  in  hours,  minutes,  and  seconds  of  time.  The  hour 
-g  then  equivalent  to  -£T  of  a  circumference,  or  15°,  and  the 

-      . 

minute  and  second  of  time  to  15'  and  15"  of  arc,  respectively. 
Thus,  an  hour  angle  of  4h2m38  equals  60°  30'  45". 


FIG.  7.  —  Hour-Circles,  etc. 


O,  place  of  the  observer  ;  Z,  his  zenith. 

SENW,  the  horizon. 

POP',  the  axis  of  the  celestial  sphere. 

P  and  P',  the  two  poles  of  the  heavens. 

EQWT,  the  celestial  equator,  or  equinoc- 
tial. 

X,  the  vernal  equinox,  or  "  first  of  Aries." 

PXP',  the  equinoctial  colure,  or  zero  hour- 
circle. 


m,  some  star. 

Ym,  the  star's  declination ;  Pm,  its  north- 
polar  distance. 

Angle  mPR  =  arc  QY,  the  star's  (eastern) 
hour  angle  ;  =  24h  minus  star's  western 
hour  angle. 

Angle  X Pm  =  arc  X  Y,  star's  right  ascension. 
Sidereal  time  at  the  moment  =  24>>  minus 
angle  XPQ. 


The  position  of  the  body  m  (Fig.  7)  is,  then,  perfectly  denned 
by  saying  that  its  declination  is  +25°  and  its  hour  angle  40°  east 
(or  simply  320°,  if  we  choose,  as  is  usual,  to  reckon  completely 
around  in  the  direction  of  the  diurnal  motion).  Instead  of  40 
degrees,  we  might  say  2h40m  of  time  east,  or  simply  21b20ra  to 
correspond  to  the  320°. 

22,  The  declination  of  a  star,  omitting  certain  minutiae  for 
the  present,  remains  practically  unaltered  even  for  years,  but 


PRELIMINARY  CONSIDERATIONS  AND  DEFINITIONS     19 

the  hour  angle  changes  continually  and  uniformly  at  the  rate  of  The  hour 
15°  for  every  sidereal  hour.     This  unfits  it  for  use  in  ephemeri-  angle 

*  changes 

des  or  star-catalogues.     We  must  substitute  for  the  meridian  continually 
some  other  hour-circle  passing  through  a   well-defined  point  ™ithtne 

9  _  tiniG  • 

which  participates  in  the  diurnal  rotation  and  so  retains  an 
unchanging  position  relative  to  the  stars.  Such  a  point, 
selected  by  astronomers  nearly  two  thousand  years  ago,  is  the 
so-called  Vernal  Equinox,  or  First  of  Aries. 

23.  The  Ecliptic,  Equinoxes,  Solstices,  and  Colures.  —  The 
sun,  moon,  and  planets,  though  apparently  carried  by  the 
diurnal  revolution  of  the  celestial  sphere,  are  not,  like  the  stars, 
apparently  fixed  upon  it,  but  move  over  its  surface  like  glow- 
worms creeping  on  a  whirling  globe.  In  the  course  of  a  year, 
as  will  be  explained  later  (Sec.  156),  the  sun  makes  a  complete 
circuit  of  the  heavens,  traveling  among  the  stars  in  a  great 
circle  called  the  Ecliptic.  The  ecliptic. 

The  ecliptic  cuts  the  celestial  equator  in  two  opposite  points 
at  an  angle  of  about  23i°.      These  points  are  the  equinoxes. 
The  Vernal  Equinox,  or  First  of  Aries  (symbol  <Y>),  is  the  point  The  vernal 
where  the   sun   crosses  from   the  south  to  the  north  side  of  the  e(1U11 
equator,  on  or  about  the   21st  of  March.      The  other  is  the 
autumnal  equinox. 

The  summer  and  winter  Solstices  are  points  on  the  ecliptic,  The  sol- 
midway  between  the  two  equinoxes  and  90°  from  each,  where  s 
the  sun  attains  its  maximum  declination  of  +  23£°  and  —  23£°     . 
in  summer  and  winter,  respectively. 

The  hour-circles  drawn  from  the  pole  (of  rotation)  through 
the  equinoxes  and  solstices  are  called  the  equinoctial  and 

solstitial    Colures.  The  colurea 

Neglecting  for  the  present  the  gradual  effect  of  pre- 
cession (Sec.  165),  these  points  and  circles  are  fixed  with 
reference  to  the  stars,  and  form  a  framework  by  which  the 
places  of  celestial  objects  may  be  conveniently  defined  and 
catalogued. 


20 


MANUAL   OF   ASTRONOMY 


Position  of 
the  vernal 
equinox. 

Definitions 
of  right 
ascension. 


The  sidereal 
day. 


Sidereal 
time. 


Definition 
of  sidereal 
time. 


No  conspicuous  star  marks  the  position  of  the  vernal  equinox ; 
but  a  line  drawn  from  the  pole-star  through  ft  Cassiopeioe  and 
continued  90°  from  the  pole  will  strike  very  near  it. 

24.  Right  Ascension. — The  Right  Ascension  of  a  star  may 
now  be  denned  as  the  angle  made  at  the  celestial  pole  between 
the    hour-circle    of  the    star    and    the    hour-circle    which  passes 
through   the    vernal    equinox  (called    the  equinoctial  colure),  or 
as  the  arc  of  the  celestial  equator  intercepted  between  the  vernal 
equinox  and  the  point  where  the  star's  hour-circle  cuts  the  equator. 
Right  ascension  is  reckoned  always  eastward  from  the  equinox, 
completely  around  the  circle,  and  may  be  expressed  either  in 
degrees  or  in  time  units.    A  star  one  degree  west  of  the  equinox 
has  a  right  ascension  of  359°,  or  23h56m. 

Evidently  the  diurnal  motion  does  not  affect  the  right  ascen- 
sion of  a  star,  but,  like  the  declination,  it  remains  practically 
unchanged  for  years.  In  Fig.  7.  (Sec.  21),  if  X  be  the  vernal 
equinox,  the  right  ascension  of  m  is  the  angle  XPm,  or  the  aro 
XY  measured  from  X  eastward. 

25.  Sidereal  Day  and  Sidereal  Time.  —  The  sidereal  day  is 
the  interval  of  time  between  two  successive  passages  of  a  fixed 
star  over  a  given  meridian,  and  at  any  place  it  begins  at  the 
moment  when  the   vernal   equinox  is  on  the  meridian;   it  is 
about  four  minutes  shorter  than  the  solar  day,  and  like  it  is 
divided  into  twenty-four  (sidereal)  hours   with  corresponding 
sidereal  minutes  and  seconds,  all  shorter  than  the  corresponding 
solar  units. 

The  sidereal  time  at  any  moment  is  the  time  shown  by  a 
clock  so  set  and  regulated  as  to  show  zero  hours,  zero  minutes, 
and  zero  seconds  at  the  moment  when  the  vernal  equinox 
crosses  the  meridian.  It  is  the  hour  angle  of  the  vernal  equinox, 
or,  what  is  the  same  thing,  the  right  ascension  of  the  observer's 
meridian. 

26.  Observatory  Definition  of  Right  Ascension.  —  The   right 
ascension  of  a  star  may  now  be  correctly,  and  for  observatory 


PRELIMINARY  CONSIDERATIONS  AND  DEFINITIONS     21 

purposes,  most  conveniently  defined  as  the  sidereal  time  at  the  Observatory 
moment  when  the  star  is  crossing  the  observer's  meridian.     Since  definitlon  of 

.  right  ascen- 

the  sidereal  clock  indicates  zero  hours  at  sidereal  noon,  i.e.,  at  sion. 
the  moment  when  the  vernal  equinox  is  on  the  meridian,  its 
face  at  any  other  time  shows  the  hour  angle  of  the  equinox ; 
and  this  is  what  has  just  been  defined  as  the  right  ascension  of 
all  stars  which  may  then  happen  to  be  on  the  meridian  (common 
to  them  all  since  they  all  lie  on  the  same  hour-circle). 


0.    SYSTEM   DETERMINED   BY   THE   PLANE    OF   THE 
EARTH'S   ORBIT 

27.    Celestial  Latitude  and  Longitude — The  ancient  astrono-  Definition 
mers  confined  their  observations  mostlv  to  the  sun,  moon,  and  of  celestial 

J  latitude  and 

planets,  which  are  never  far  from  the  ecliptic,  and  for  this  longitude, 
reason  the  ecliptic  (which  is  simply  the  trace  of  the  plane  of  the 
earth's  orbit  upon  the  celestial  sphere)  was  for  them  a  more 
convenient  circle  of  reference  than  the  equator,  —  especially  as 
they  had  no  accurate  clocks.  According  to  their  terminology, 
Latitude  (celestial)  is  the  angular  distance  of  a  heavenly  body 
north  or  south  of  the  ecliptic ;  Longitude  (celestial)  is  the  arc 
of  the  ecliptic  intercepted  between  the  vernal  equinox  (°f )  and 
the  foot  of  a  circle  drawn  from  the  pole  of  the  ecliptic  to  the 
ecliptic  through  the  object.  Longitude,  like  right  ascension,  is 
always  reckoned  eastward  from  the  equinox. 

Circles  drawn  from  the  poles  of  the  ecliptic  perpendicular  to 
the    ecliptic   are   called  secondaries  to  the   ecliptic,  —  by  some  Secondaries 
writers  "  ecliptic  meridians,"  and  on-  some  celestial  globes  are  to  the 

ecliptic. 

drawn  instead  of  hour-circles. 

The  poles  of  the  ecliptic  are  the  points  90°  distant  from  the  Poles  of  the 
ecliptic.     The  position  of  the  north  ecliptic  pole  is  shown  in  ecllPtlc- 
Fig.  4.     It  is  on  the  solstitial  colure,  about  231-0  distant  from 
the  pole  of  rotation,  in  declination  66J-0  and  right  ascension 
18h.     It  is  marked  by  no  conspicuous  star. 


22 


MANUAL   OF   ASTRONOMY 


It  is  unfortunate,  or  at  least  confusing  to  beginners,  that  celes- 
tial latitude  and  longitude  should  not  correspond  with  the  ter- 
restrial quantities  that  bear  the  same  name.  Great  care  must 
be  taken  to  observe  the  distinction. 


The  gravity 
system  of 
coordinates. 


The  two 
systems 
which  de- 
pend upon 
the  rotation 
of  the  earth. 


28.  Recapitulation.  —  The  direction  of  gravity  at  the  point 
where  the  observer  happens  to  stand  determines  the  zenith  and 
nadir,  the  horizon  and  the  almucantars,  or  parallels  of  altitude, 
and  all  the  vertical  circles.  One  of  the  verticals,  the  meridian, 
is  singled  out  from  the  rest  by  the  circumstance  that  it  is  the 
projection  of  the  observer's  terrestrial  meridian  upon  the  celestial 
sphere  and  passes  through  the  pole,  marking  the  north  and  south 
points  where  it  cuts  the  horizon.  Altitude  and  azimuth,  or  their 
complements,  zenith-distance  and  amplitude,  define  the  position 
of  a  body  by  reference  to  the  horizon  and  meridian. 

This  set  of  points  and  circles  shifts  its  position  among  the 
stars  with  every  change  in  the  place  of  the  observer  and  every 
moment  of  time.  Each  place  and  hour  has  its  own  zenith,  its 
own  horizon,  and  its  own  meridian. 

In  a  similar  way,  the  direction  of  the  earths  axis,  which  is 
independent  of  the  observer's  place  on  the  earth,  determines  the 
pole  (of  rotation),  the  equator,  parallels  of  declination,  and  the 
hour-circles.  Two  of  these  hour-circles  are  singled  out  as 
reference  lines:  one  of  them  is  the  hour-circle  which  at  any 
moment  passes  through  the  zenith  and  coincides  with  the  merid- 
ian, —  a  purely  local  reference  line ;  the  other,  the  equinoctial 
colure,  which  passes  through  the  vernal  equinox,  a  point  chosen 
from  its  relation  to  the  sun's  annual  motion. 

Declination  and  hour  angle  define  the  place  of  a  star  with 
reference  to  the  equator  and  meridian,  while  declination  and 
right  ascension  refer  it  to  the  equator  arid  vernal  equinox.  The 
latter  are  the  coordinates  usually  given  in  star-catalogues  and 
almanacs  for  the  purpose  of  defining  the  position  of  stars  and 
planets,  and  they  correspond  exactly  to  latitude  and  longitude  on 


PRELIMINARY  CONSIDERATIONS  AND  DEFINITIONS     23 


the  earth,  by  means  of  which  geographical  positions  are  desig- 
nated.     °f  in  the  sky  takes  the  place  of  Greenwich  on  the  earth. 

Finally,  the  earth's  orbit  gives  us  the  great  circle  of  the  sky  The  ecliptic 
known  as  the  ecliptic  ;  and  celestial  latitude  and  longitude  define  system- 
the  position  of  a  star  with  reference  to  the  ecliptic  and  the  ver- 
nal equinox  (°p ).     For  most  purposes  this  pair  of  coordinates  is 
practically  less  convenient  than  right  ascension  and  declination ; 
but  it  came  into  use  centuries  earlier,  and  has  advantages  in 
dealing  with  the  planets  and  the  moon. 

29,  The  scheme  given  below  presents  in  tabular  form  the 
relations  of  the  four  different  systems  to  each  other.  In  each 
case  one  of  the  two  coordinates  is  measured  along  a  primary 
circle,  from  a  point  selected  as  the  origin,  to  a  point  where  a 
secondary  circle  cuts  it,  drawn  through  the  object  perpendicular 
to  the  primary.  The  second  coordinate  is  the  angular  distance 
of  the  object  from  the  primary  circle  measured  along  this 
secondary. 


SYS- 
TEM 

PRIMARY  CIR- 
CLE, HOW 

DETERMINED 

PRIMARY 
CIRCLE 

ORIGIN 

SECONDARY 
CIRCLE 

COORDI- 
NATES 

USUAL 
SYMBOL 

X  £i  ffi  H 

A 

Direction  of 
gravity 

Horizon 

South  point 
on  horizon 

Vertical  cir- 
cle of  star 

Azimuth 
Altitude 

c 

(A) 

<w 

B« 

"  1 

Rotation  of 
earth 

Celestial 
equator 

Foot  of  the 
meridian  on 
equator 

Hour-circle 
of  star 

Hour  angle 
Declination 

<** 

(5) 

2 

Rotation  of 
earth 

Celestial 
equator 

The  vernal 
equinox  (°f) 

Hour-circle 
of  star 

Right  ascen- 
sion 
Declination 

(«) 

(5) 

C 

Plane  of 
earth's  orbit 

Ecliptic 

The  vernal 
equinox  (°f3) 

Secondary  to 
ecliptic 
through  star 

Longitude 
Latitude 

(X) 
08)' 

Tabular 
exhibit  of 
the  four 
systems  of 
coordinates 


30.    Relation  of  the  Coordinates  on  the  Sphere.  —  Fig.  8  shows  how  these  Diagram 

coordinates    are    related    to    each  other.     The  reader   is  supposed  to  be  showing  the 

looking  down  on  the  celestial  sphere  from  above,  the  circle  SENWA  being  relation  of 
the  horizon. 


the  systems. 


24 


MANUAL   OF   ASTRONOMY 


Z  is  the  zenith ;  P,  the  north  pole  (of  rotation) ;  P',  the  pole 
of  the  ecliptic  ;  °f  ,  the  vernal  equinox,  and  £^,  the  autumnal ;  S,  E,  N,  W 
are  the  cardinal  points  of  the  horizon.  The  oval  W^MQCE-^R  is 
the  celestial  equator,  and  the  narrower  one,  °fLB±±K,  is  the  ecliptic. 
The  angle  B°fC,  measured  by  the  arcs  EC  and  PP',  is  the  obliquity  of  the 
ecliptic,  for  which  the  usual  symbol  is  e  or  c. 

O  is  some  celestial  object.  Then  the  arc  A  0  (projected  as  a  straight 
line)  is  its  altitude  and  the  angle  OZS  its  azimuth.  OM  is  its  declination 


FIG.  8.  —Relation  of  the  Different  Coordinates 


and  OPQ,  its  hour  angle.  °fPMis  its  right  ascension  =  arc  °f  M.  OL  is  its 
latitude  and  °f  P'L  (-  arc  °f  L)  is  its  longitude.  °f  P  is  90°  of  the  equi- 
noctial colure  and  P'PBC  is  part  of  the  solstitial  colure.  The  angles  °f>  P'B 
and  TPC"  are  each  90°. 

For  methods  and  formulae  by  which  either  set  of  coordinates  may  be 
"transformed"  into  one  of  the  others,  see  Sees.  700  and  701  (Appendix). 


PRELIMINARY  CONSIDERATIONS  AND  DEFINITIONS     25 


31.  The  Astronomical  Triangle.  —  The  triangle  PZO  (pole- 
zenith-object)  (Fig.  8)  is  often  called  the  astronomical  triangle 
because  so  many  problems,  especially  of  nautical  astronomy, 
depend  on  its  solution.     Its  sides  and  angles  are  all  named,  — 
PZ  is  the  colatitude  of  the  observer,  ZO  is  the  zenith-distance  of 
the  object,  and  OP  is  its  north  polar  distance,  or  complement  of 
its  declination.     The  angle  P  is  the  hour  angle  of  the  object,  the 
angle  Z  is  the  supplement  of  its  azimuth,  and,  finally,  the  angle 
at  0  is  called  the  parallac- 

tic  angle,  because  it  enters 
into  the  calculations  of  the 
effects  of  parallax  and  re- 
fraction upon  the  right 
ascension  and  declination 
of  a  body.  Any  three  of 
the  parts  being  given  the 
others  can,  of  course,  be 
found. 

32.  Relation  of  the  Place 
of  the  Celestial  Pole  to  the 
Observer's    Latitude.  --If 

an  observer  were  at  the  north  pole  of  the  earth,  it  is  clear  that 
the  pole-star  would  be  very  near  his  zenith,  while  it  would  be 
at  his  horizon  if  he  were  at  the  equator.  The  place  of  the  pole 
in  the  sky,  therefore,  depends  entirely  on  the  observer's  latitude, 
and  in  this  very  simple  way  the  altitude  of  the  pole  (its  height 
in  degrees  above  the  horizon)  is  always  equal  to  the  latitude 
of  the  observer.  This  will  be  clear  from  Fig.  9.  The  latitude 
(astronomical)  of  a  place  may  be  defined  as  the  angle  between  the 
direction  of  gravity  at  that  place  and  the  plane  of  the  earths 
equator,  —  the  angle  ONQ  in  Fig.  9.  If  at  0  we  draw  HH1  per- 
pendicular to  ON,  it  will  be  a  level  line,  and  will  lie  in  the 
plane  of  the  horizon.  From  0  also  draw  OP"  parallel  to  CPf,  the 
earth's  axis.  OP"  and  CPf,  being  parallel,  will  both  be  directed 


The  "astro- 
nomical 
triangle." 


FIG.  9.  —  Relation  of  Latitude  to  the 
Elevation  of  the  Pole 


Position  of 
the  pole  in 
the  sky. 


The  altitude 
of  the  pole 
equals  the 
observer's 
latitude. 


26  MANUAI,    OF   ASTRONOMY 

to  their  "vanishing   point"  in  the  celestial   sphere   (Sec.  7), 

which  is  the  celestial  pole.     The  angle  H'OP"  is  therefore  the 

altitude  of  the  pole  as  seen  at  0 ;  and  it  obviously  equals  ONQ. 

This  fundamental  relation,  that  the  altitude  of  the  pole  is  identical 

with  the  observer's  latitude,  cannot  be  too  strongly  emphasized. 

Aspect  of  33.   The  Right  Sphere.  —  If  the  observer  is  situated  at  the 

the  heavens    eartn's  equator,  that  is,  in  latitude  zero,  the  pole  will  be  in  his 

as  seen  from 

the  earth's  horizon  and  the  celestial  equator  will  be  a  vertical  circle,  coin- 
equator,  ciding  with  the  prime  vertical  (Sec.  14).  All  heavenly  bodies 
will  rise  and  set  vertically,  and  their  diurnal  circles  will  all  be 
bisected  by  the  horizon,  so  that  they  will  be  twelve  hours  above 
and  twelve  hours  below  it ;  and  the  length  of  the  night  will 
always  equal  that  of  the  day  (neglecting  refraction,  Sec.  82). 
This  aspect  of  the  heavens  is  called  the  right  sphere. 

It  is  worth  noting  that  for  an  observer  exactly  at  the  north  pole  the 
definitions  of  meridian  and  azimuth  break  down,  since  at  that  point  the 
zenith  coincides  with  the  pole.  Facing  which  direction  he  will,  he  is 
still  looking  directly  south.  If  he  change  his  place  a  few  steps,  how- 
ever, his  zenith  will  move,  and  everything  will  become  definite  again. 

Aspect  of  34.   The  Parallel  Sphere.  —  If  the  observer  is  at  the  pole  of 

the  heavens   the  earth  where  hig  latitude  is  990   the  celestial  pole  will  be 

as  seen  from 

the  pole.  at  his  zenith  and  the  equator  will  coincide  with  the  horizon. 
If  at  the  north  pole,  all  the  stars  north  of  the  celestial  equator 
will  remain  permanently  above  the  horizon,  never  rising  nor 
falling,  but  sailing  around  the  sky  on  almucantars,  or  parallels 
of  altitude.  The  stars  in  the  southern  hemisphere,  on  the 
other  hand,  will  never  rise  to  view. 

Since  the  sun  and  moon  move  among  the  stars  in  such  a 
way  that  during  half  of  the  time  they  are  north  of  the  equator 
and  half  the  time  south  of  it,  they  will  be  half  the  time  above 

The  six         the  horizon  and  half  the  time  below  it,  at  least  approximately, 
*7  S*nce  ^S  statement  nee(ls  to  be  slightly  modified  to  allow  for  the 
effect  of  refraction.     The  moon  will  be  visible  for  about  a  fort- 
night each  month  and  the  sun  for  about  six  months  each  year. 


PRELIMINARY  CONSIDERATIONS  AND  DEFINITIONS     27 


35.  The  Oblique  Sphere.  —  At  any  station  between  the  poles 
and  the  equator  the  pole  will  be  elevated  above  the  horizon, 
and  the  stars  will  rise  and  set  in  oblique  circles,  as  shown  in 
Fig.  10.     Those  whose  distance  from  the  elevated  pole  is  less 
than  PN  (the  latitude  of  the  observer)  will  of  course  never  set, 
remaining  perpetually  visible.     The  radius  of  this  circle  of  per- 
petual apparition,  as  it  is  called  (the  shaded  cap  around  P  in 
the  figure),  is  obviously  just  equal  to  the  height  of  the  pole, 
becoming  larger  as  the  latitude  increases.     On  the  other  hand, 
stars  within  the  same  distance 

of  the  depressed  pole  will  lie 
in  the  circle  of  perpetual  occul- 
tation,  and  will  never  rise 
above  the  horizon.  A  star 
exactly  on  the  celestial  equa- 
tor will  have  its  diurnal  circle 
bisected  by  the  horizon  and 
will  be  above  the  horizon 
twelve  hours.  A  star  north 
of  the  equator,  if  the  north 
pole  is  the  elevated  one,  will 
have  more  than  half  its  diur- 
nal circle  above  the  horizon 
and  will  be  visible  for  more  than  twelve  hours  each  day;  as, 
for  instance,  a  star  at  A,  rising  at  B  and  setting  at  B1. 

Whenever  the  sun  is  north  of  the  celestial  equator,  the  day 
will  therefore  be  longer  than  the  night  for  all  stations  in  north- 
ern latitude ;  how  much  longer  will  depend  on  the  latitude  of 
the  place  and  the  sun's  distance  from  the  equator,  i.e.,  its 
declination. 

36.  The  Midnight  Sun.  —  If  the  latitude  of  the  observer  is 
such  that  PN  in  the  figure  is  greater  than  the  sun's  polar 
distance   or   codeclination  at  the  time  when   the   sun  is  far- 
thest north  (about  66 J°),  the  sun  will  come  into  the  circle  of 


FIG.  10.  — The  Oblique  Sphere 


The  mid- 
night sun. 


28 


MANUAL   OF   ASTRONOMY 


When  the 

sun  shines 
into  north 
windows. 


perpetual  apparition  and  will  make  a  complete  circuit  of  the 
heavens  without  setting,  until  its  polar  distance  again  becomes 
less  than  PN.  This  happens  near  the  summer  solstice  at  the 
North  Cape  and  at  all  stations  within  the  Arctic  circle. 

Whenever  the  sun  is  north  of  the  equator  it  will  in  all  north 
latitudes  rise  at  a  point  north  of  east,  as  B  in  the  figure,  and 
will  continue  to  shine  upon  every  vertical  surface  that  faces 
the  north,  until,  as  it  ascends,  it  crosses  the  prime  vertical 
EZW  at  some  point  V. 

In  the  latitude  of  New  York,  the  sun  on  the  longest  days  of  summer 
is  south  of  the  prime  vertical  only  about  eight  hours  of  the  whole  fifteen 
during  which  it  is  above  the  horizon.  During  seven  hours  of  the  day  it 
shines  into  north  windows. 


The  celestial 
globe. 


Its  horizon 
and  circles 
upon  it. 


The  merid- 
ian ring,  its 
graduation 
and  clamp. 


A  celestial  globe  will  be  of  great  assistance  in  studying 
these  diurnal  phenomena.  By  means  of  this  it  can  at  once 
be  seen  what  stars  never  set,  which  ones  never  rise,  and 
during  what  part  of  the  twenty-four  hours  a  heavenly  body 
at  a  known  declination  is  above  or  below  the  horizon. 

37.  The  Celestial  Globe.  —  The  celestial  globe  is  a  ball,  usually  of 
papier-mach£,  upon  which  are  drawn  the  circles  of  the  celestial  sphere 
and  a  map  of  the  stars.  It  is  mounted  in  a  framework  which  represents 
the  horizon  and  the  meridian,  in  the  manner  shown  by  Fig.  11. 

The  horizon,  HH'  in  the  figure,  is  usually  a  wooden  ring  three  or  four 
inches  wide,  directly  supported  by  the  pedestal.  It  carries  upon  its  upper 
surface  at  the  inner  edge  a  circle  marked  with  degrees  for  measuring  the 
azimuth  of  any  heavenly  body,  and  outside  this  the  so-called  "zodiacal 
circles,"  which  give  the  sun's  longitude  and  the  equation  of  time  (Sees.  99 
and  174)  for  every  day  of  the  year. 

The  meridian  ring,  MM',  is  a  circular  ring  of  metal  which  carries  the 
bearings  of  the  axis  on  which  the  globe  revolves.  Things  are  so  arranged, 
or  ought  to  be,  that  the  mathematical  axis  of  the  globe  is  exactly  in  the 
same  plane  as  the  graduated  face  of  the  ring,  which  is  divided  into  degrees 
and  fractions  of  a  degree,  with  zero  at  the  equator.  The  meridian  ring 
fits  into  two  notches  in  the  horizon  circle  and  is  held  underneath  the  globe 


PRELIMINARY  CONSIDERATIONS   AND  DEFINITIONS     29 


by  a  support  with  a  clamp,  which  enables  us  to  fix  it  securely  in  any 
desired  position,  the  mathematical  center  of  the  globe  being  precisely  in 
the  planes  both  of  the  meridian  ring  and  the  horizon. 

The  hour  index  on  the  globe  here  figured  is  a  pointer  like  the  hour-hand 
of  a  clock,  so  attached  to  the  meridian  ring  at  the  pole  that  it  can  be 
turned  around  the  axis  with  stiffish  friction,  but  will  retain  its  position 
unchanged  when  the  globe  is  made  to  turn  under  it.  It  points  out  the 
time  on  a  small  time-circle  graduated  usually  to  hours  and  quarters  printed 
on  the  surface  of  the  globe. 

The  surface  of  the  globe  is  marked  first  with  the  celestial  equator  (Sec.  20), 
next  with  the  ecliptic  (Sec.  23),  crossing  the  equator  at  an  angle  of 
23^°  (at  X  in  the  figure),  and 
each  of  these  circles  is  divided 
into  degrees  and  fractions. 
The  equinoctial  and  solstitial 
colures  (Sec.  23)  are  also  al- 
ways represented.  As  to  the 
other  circles,  usage  differs. 
The  ordinary  way  at  present 
is  to  mark  the  globe  with 
twenty-four  hour-circles,  fif- 
teen degrees  apart  (the  colures 
being  two  of  them),  and  with 
parallels  of  declination  ten 
degrees  apart. 

On  the  surface  of  the  globe 
are  plotted  the  positions  of  the 
stars  and  the  outlines  of  the 
constellations. 

38.  To  rectify  a  globe,  — 
that  is,  to  set  it  so  as  to 
show  the  aspect  of  the  heavens  at  any  given  time, — 

(1)  Elevate  the  north  pole  of   the  globe  to   an  angle  equal   to   the 
observer's  latitude  by  means  of  the  graduation  on  the  meridian  ring,  and 
clamp  the  ring  securely. 

(2)  Look  up  the  day  of  the  month  on  the  horizon  of  the  globe  and 
opposite  to  the  day  find,  on  the  longitude  circle,  the  sun's  longitude  for 
that  day. 

(3)  On  the  ecliptic  (on  the  surface  of  the  globe)  find  the  degree  of  longi- 
tude thus  indicated  and  bring  it  to  the  graduated  face  of  the  meridian  ring. 


FIG.  11.  — The  Celestial  Globe 


The  hour 
index. 


Circles 
drawn  on 
surface  of 
globe. 


30 


MANUAL   OF   ASTRONOMY 


The  globe  is  then  set  to  correspond  to  (apparent)  noon  of  the  day  in 
question.  (It  may  be  well  to  mark  the  place  of  the  sun  temporarily  with 
a  bit  of  moist  paper  applied  at  the  proper  place  in  the  ecliptic ;  it  can 
easily  be  wiped  off  after  using.) 

(4)  Holding  the  globe  fast,  so  as  to  keep  the  place  of  the  sun  on  the 
meridian,  turn  the  hour  index  until  it  shows  on  the  graduated  time-circle  the 
local  mean  time  of  apparent  noon,  i.e.,  12h  ±  the  equation  of  time  given  for 
the  day  on  the  horizon  ring.     (If  standard  time  is  used,  the  hour  index  must 
be  set  to  the  standard  time  of  apparent  noon.) 

(5)  Finally,  turn  the  globe  until  the  hour  for  which  it  is  to  be  set  is 
brought  to  the  meridian,  as  indicated  on  the  hour  index.     The  globe  will 
then  show  the  true  aspect  of  the  heavens. 

The  positions  of  the  moon  and  planets  are  not  given  by  this  operation, 
since  they  have  no  fixed  places  in  the  sky  and  therefore  cannot  be  put  upon 
the  globe  by  the  maker.  If  one  wants  them  represented,  he  must  look  up 
their  right  ascensions  and  declinations  for  the  day  in  some  almanac  and 
mark  the  places  on  the  globe  with  bits  of  wax  or  paper. 


EXERCISES 

1.  What  point  in  the  celestial  sphere  has  both  its  right  ascension  and 
declination  zero  ?    ^"jf^ 

2.  What  are  the  celestial  latitude  and  longitude  of  this  poin^t?   "Q 

3.  What  are  the  hour  angle'  and  azimuth  of  the  zenith  ?  hyW 

4.  At  what  points  does  the  celestial  equator  cut  the  horizon?^ 

5.  What  angle  does  the  celestial  equator  make  with  the  horizon  at 
these  points,  as  seen  by  an  obsgryerAin  latitude  40°?      J   Dl 

6.  What  if  his  latitude  is  10°f  20°?  50°V '60°^° 

7.  When  the  vernal  equinox  °f°  is  rising  on  the  eastern  horizon,  what 
angle  does  the  ecliptic  make  with  the  horizon  at  that  point  for  an  observer 
in  latitude  40°?    ^^3" 

8.  What  angle  when  setting  ? 

9.  What  is  the  angle  between  the   ecliptic  and  horizon  when  the 
autumnal  equinox  is  rising,  and  when  setting? 

10.  Name  the  fourteen  principal  points  on  the  celestial  sphere  (zenith, 
poles,  equinoxes,  etc.). 

11.  What  important  circles  on  the  celestial  sphere  have  no  correlatives 
on  the  surface  of  the  earth  ? 


PRELIMINARY  CONSIDERATIONS  AND  DEFINITIONS     31 

12.  What  are  the  approximate  right  ascension  and  declination  (a  and  8) 
of  the  sun  on  March  21  and  September  22? 

13.  What  is  the  sun's  altitude  at  noon  on  March  21  for  an  observer  in 
latitude  42°?     C/C 

14.  How  far  is  the  sun  from  the  zenith  at  noon  on  March  21,  as  seen 
at  Pulkowa,  latitude  60°?     How  far  at  noon  on  June  21  ? 

15.  On  March  21,  one  hour  after  sunset,  whereabouts  in  the  sky  would 
be  a  star  having  a  right  ascension  of  7  hours  and  declination  of  40°,  the 
observer  being  in  latitude  40°  ? 

16.  If  a  star  rises  to-night  at  10  o'clock,  at  what  time  (approximately) 
will  it  rise  30  days  hence  ? 

17.  When  the  right  ascension  of  the  sun  is  6  hours,  what  are  its  longi- 
tude (A)  and  latitude  (0)  ? 

18.  What,  when  its  a  is  12  hours? 

19.  What  are  the  latitude  and  longitude  of  the  north  pole  of  rotation  ? 

20.  What  are  the  right  ascension  and  declination  of  the  north  pole  of 
the  ecliptic  ? 

NOTE.  — None  of  the  above  exercises  require  any  calculation  beyond  a  simple 
addition  or  subtraction. 

21.  What  are  the  longitude  and  declination  of  the  sun  when  its  right 

ascension  is  3  hours  ? 

An§     (  Long.  =  47°  27'  59". 

<  Dec.     =  17°  03'  08". 

NOTE.  —  This  requires  the  solution  of  the  spherical  right  angle  triangle,  in  which 
the  base  is  the  given  a  (=45°),  the  angle  adjacent  is  e  (23°  IT),  and  the  parts  to  be 
found  are  the  hypotenuse  X  and  the  other  leg  opposite  c,  which  is  5. 


CHAPTER   II 
ASTRONOMICAL   INSTRUMENTS 

Telescopes,  and  their  Accessories  and  Mountings  —  Timekeepers  and  Chronographs 

—  The  Transit-Instrument  —  The  Prime  Vertical  Instrument  —  The  Almucantar 

—  The    Meridian-Circle    and    Universal    Instrument  —  The    Micrometer  —  The 
Heliometer  — The  Sextant 

39.  Astronomical  observations  are  of  various  kinds  :  some- 
times we  desire  to  ascertain  the  apparent  distance  between  two 
bodies ;  sometimes  the  position  which  the  body  occupies  at  a 
given  time,  or  the  time  at  which  it  arrives  at  a  given  circle  of 
the  sky,  —  usually  the  meridian.     Sometimes  we  wish  merely 
to  examine  its  surface,  to  measure  its  light,  or  to  investigate 
its  spectrum;   and  for  all  these  purposes  special  instruments 
have  been  devised.     We  propose  in  this  chapter  to  describe  a 
few  of  the  most  important  at  present  in  use. 

40.  Telescopes  in  General. -- Telescopes  are   of  two   kinds, 
refracting   and    reflecting.      The    former   were    first   invented 
and  are  much  more  used,  but  the  largest  instruments  which 

Fundamental  have  ever  been  made  are  reflectors.  In  both  the  fundamental 
Principle  is  identical.  The  large  lens,  or  mirror,  —  the  "object- 
ive "  of  the  instrument  —  forms  at  its  focus  a  "  real "  image 
of  the  object  looked  at,  and  this  image  is  then  examined 
and  magnified  by  the  eyepiece,  which"  in  principle  is  only  a 
magnify  ing-glass. 

Essential  41.    The  Simple  Refracting  Telescope.  —  This  consists  essen- 

thTrefrac^  ^ally,  as  shown  in  Fig.  12,  of  two  convex  lenses,  one  the  object- 
ing tele-  glass  A,  of  large  size  and  long  focus ;  the  other,  the  eyepiece 
scope.  ^  o;f  short  focus  ;  the  two  being  set  at  a  distance  nearly  equal  to 

the  sum  of  their  focal  lengths.     Recalling  the  optical  principles 


ASTRONOMICAL   INSTRUMENTS 


33 


of   the    formation    of   images    by  lenses,1  we   see   that  if   the 

instrument  is  pointed  toward  the  moon,  for  instance,  all  the 

rays  that  strike  the  object-glass  from  the  top  of  the  object  will 

come  to  a  focus  at  a,  while  those  from  the  bottom  will  come  to 

a  focus  at  &,  and  similarly  with  rays  from  other  points  on  the 

surface  of  the  moon.     We   shall  therefore  get  in  the  "focal  Real  image 

plane  "  of  the  object-glass  a  small  inverted  "  real "  image  of  the 

moon,  so  that  if  a  photographic  plate  is  inserted  in  the  focal 

plane  at  ab  and  properly  exposed,  we  shall  get  a  picture  of  the 

object. 

The    size    of   the    picture    will    depend  upon   the    apparent  Size  of  the 
angular  diameter  of  the  object  and  the  distance  of  the  image 
ab  from  the  object-glass,   and  is  determined  by  the  condition 


FIG.  12. —  The  Simple  Refracting  Telescope 

that,  as  seen  from  point  0  (the  optical  center  of  the  object-glass), 
the  object  and  its  image  subtend  equal  angles,  since  rays  which 
pass  through  the  point  0  suffer  no  sensible  deviation. 

If  the  focal  length  of  the  lens  A  is  10  feet,  then  the  image  of  the  moon 
formed  by  it  will  appear,  when  viewed  from  a  distance  of  10  feet,  just  as 
large  as  the  moon  itself  ;  from  a  distance  of  1  foot,  the  image  will,  of 
course,  appear  ten  times  as  large 

With  such  an  object-glass,  therefore,  even  without  an  eyepiece,  one 
can  see  the  mountains  of  the  moon  and  satellites  of  Jupiter  by  simply 
putting  the  eye  in  the  line  of  the  rays,  at  a  distance  of  10  or  12  inches 
back  of  the  eyepiece  hole,  the  eyepiece  itself  having  been,  of  course, 
removed.  • 

1  In  this  explanation  we  use  the  approximate  theory  of  lenses  (in  which 
their  thickness  is  neglected),  as  given  in  the  elementary  text-books.  The  more 
exact  theory  would  require  some  slight  modification  in  statements,  but  none  of 
substantial  importance. 


34  MANUAL   OF   ASTRONOMY 

42.  Magnifying  Power.  —  If  we  use  the  naked  eye,  one 
cannot,  unless  near-sighted,  see  the  image  distinctly  from  a 
distance  much  less  than  10  inches;  but  if  we  use  a  magnifying- 
lens  of  1-inch  focus,  we  can  view  it  from  a  distance  of  only 
an  inch,  and  it  will  look  correspondingly  larger.  Without 
stopping  to  demonstrate  the  principle,  the  magnifying  power  is 
simply  equal  to  the  quotient  obtained  by  dividing  the  focal  length 
of  the  object-glass  by  that  of  the  eye-lens  ;  or,  as  a  formula, 

Formula  for 

themagni-  M  —  F/f\  that  is,  Od/cd  in  the  figure. 

f  ying  power. 

If,  for  example,  the  focal  length  of  the  object-glass  be  4  feet 
and  that  of  the  eye-lens  one  quarter  of  an  inch,  then 

M=  48  •*•  J  =4x48  =  192. 

A  magnifying  power  of  unity,  however,  is  often  spoken  of  as  "  no  magni- 
fying power  at  all,"  since  the  image  appears  of  the  same  size  as  the  object. 

The  magnifying  power  of  the  telescope  is  changed  at  pleasure  by  simply 
changing  the  eyepiece  (see  Sec.  47). 

Light-gath-        43.    Light-Gathering  Power  of  the  Telescope  and  Brightness 

ering  power   Of  the  Image This  depends  not  upon  the  focal  length  of  the 

to  the  square  object-glass,  but  upon  its  diameter;  or,  more  strictly,  its  area. 

of  the  diam-  If  we  estimate  the  diameter  of  the  pupil  of  the  eye  at  one  fifth 

object-glass    °^  an  ^ncn'  then  (neglecting  the  loss  in  transmission  through 

the  lenses)  a  telescope  1   inch  in  diameter  collects  into  the 

image  of  a  star  twenty-five  times  as  much  light  as  the  naked 

eye  receives;   and    the    great  Yerkes    telescope   of   40  inches 

in  diameter  gathers    40000   times    as   much,  or  about  35000 

after  allowing  for  the  losses.     The  amount  of  light  collected  is 

proportional  to  the  square  of  the  diameter  of  the  object-glass. 

The  apparent  brightness  of  an  object  which,  like  the  moon  or 
a  planet,  shows  a  disk,  is  not,  however,  increased  in  any  such 
ratio,  because  the  light  gathered  by  the  object-glass  is  spread 
out  by  the  magnifying  power  of  the  eyepiece.  In  fact,  it  can  be 
demonstrated  that  no  optical  arrangement  whatever  can  show 


ASTRONOMICAL   INSTRUMENTS  35 

an  extended  surface  brighter  than  it  appears  to  the  naked  eye.  No  optical 
But  the  total  quantity  of  light  in  the  image  of  the  object  greatly  arranse- 
exceeds  that  which  is  available  for  vision  with  the  naked  eye,  increase  the 
and  objects  which,  like  the  stars,  are   mere   luminous  points,  intrinsic 
have  their  brightness  immensely  increased,  so  that  with  the  tele-  Of  j^** 
scope  millions  otherwise  invisible  are  brought  to  light.     With  the  extended 
telescope,  also,  the  brighter  stars  are  easily  seen  in  the  daytime.  s 

44.    The  Achromatic  Telescope.  —  A  single  lens  cannot  bring  Chromatic 
the  rays  which  emanate  from  a  single  point  in  the  obiect  to  anv  aberration 

.  *f  J     of  a  single- 

exact  locus,  since  the  rays  01  different  color  (wave-length)  are  lens  object- 
differently  refracted,  the  blue  more  than  the  green,  and  this  glass- 
more  than  the  red.     In  consequence  of  this  so-called  "  chromatic 
aberration,"  the  simple  refract- 
ing  telescope    is    a  very  poor 
instrument.1  r7ZT^   u  Lutrow 

About  1760   it  was  discov- 
ered  in  England  that  by  making         FIG.  13.  —  Different  Forms  of  the 
the  object-glass  of  two  or  more 

lenses  of  different  kinds  of  glass  the  chromatic  aberration  can 
be  nearly  corrected.  Object-glasses  so  made  —  no  others  are 
now  in  common  use  —  are  called  achromatic,  and  they  fulfil  The  achro- 
with  reasonable  approximation,  though  not  perfectly,  the  con-  matiolens- 
dition  of  distinctness  ;  namely,  that  the  rays  which  emanate 
from  any  single  point  in  the  object  should  be  collected  to  a 
single  point  in  the  image.  In  practice,  only  two  lenses  are 
ordinarily  used  in  the  construction  of  an  astronomical  object- 
glass,  —  a  convex  of  crown-glass,  and  a  concave  of  flint-glass, 
the  curves  of  the  two  lenses  and  the  distances  between  them 
being  so  chosen  as  to  give  the  best  possible  correction  of  the 

1  By  making  the  telescope  extremely  long  in  proportion  to  its  diameter,  the 
distinctness  of  the  image  is  considerably  improved,  and  in  the  middle  of  the 
seventeenth  century  instruments  more  than  200  feet  in  length  were  used  by 
Cassini  and  others.  Saturn's  rings  and  several  of  his  satellites  were  discovered 
by  Huyghens  and  Cassini  with  instruments  of  this  kind. 


36 


MANUAL   OF   ASTRONOMY 


Imperfect 
achroma- 
tism of 
object- 


More  perfect 
object 
lenses  from 
new  kinds 
of  glass. 


The  spuri- 
ous disk  of 
a  star. 


spherical  aberration  as  well  as  of  the  chromatic.     Many  forms 
of  object-glass  are  made,  three  of  which  are  shown  in  Fig.  13. 

45.  Secondary   Spectrum.  —  It  is    not   possible    to   obtain  a 
perfect  correction  of  color  with  the  only  kinds  of  glass  which 
were  available  until  very  recently.     Ordinary  achromatic  lenses, 
even  the  best  of  them,  show  around  every  bright  object  a  strong 
purple  halo,  due  to  red  and  blue  rays  which  are  both  brought 
to  a  focus  further  from  the  object-glass  than  are  the  yellow  and 
green.     This  halo  seriously  injures  the  definition  and  makes  it 
difficult  to  see  small  stars  very  near  a  bright  one.    It  is  specially 
obnoxious  in  large  instruments. 

Much  is  hoped  from  the  new  varieties  of  glass  now  being 
made  at  Jena  in  Germany.  Several  telescopes  of  considerable 
size  have  already  been  constructed,  of  which  the  lenses  are 
practically  aplanatic;  that  is,  sensibly  free  from  both  spherical 
and  chromatic  aberration.  Possibly  a  new  era  in  telescope 
making  is  opening  with  the  new  century. 

46.  Diffraction  and  Spurious  Disks.  —  Even  if  a  lens  were 
absolutely   perfect   as    regards    the    correction    of   aberrations, 
it   would   still   be    unable    to  fulfil    strictly  the    condition   of 
distinctness. 

Since  light  consists  of  waves  of  finite  length,  the  image  of  a 
luminous  point  can  never  be  also  a  point,  but  necessarily,  on 
account  of  "  diffraction,"  consists  of  a  central  disk  of  finite 
diameter,  surrounded  by  a  series  of  "  interference  "  rings ;  and 
the  image  of  a  line  is  a  streak  and  not  a  line.  The  diameter 
of  the  "  spurious  disk  "  of  a  star,  as  it  is  called,  varies  inversely 
with  the  diameter  of  the  object-glass  ;  the  larger  the  telescope,  the 
smaller  the  image  of  a  star  with  a  given  magnifying  power. 

With  a  good  41-inch  telescope  and  a  power  of  about  120,  the 
image  of  a  small  star,  when  the  air  is  perfectly  steady  (which 
unfortunately  seldom  happens),  is  a  clean,  round  disk,  about  1" 
in  diameter,  with  a  bright  ring  around  it,  separated  from  the 
disk  by  a  dark  space  about  as  wide  as  the  disk.  With  a  9-inch 


ASTRONOMICAL   INSTRUMENTS  37 

instrument  the  disk  has  a  diameter  of  0".5, —  just  half  as  great ; 
with  the  Yerkes  telescope,  about  0".ll.  The  angular  diameter 
of  a  star  disk  in  a  telescope  the  aperture  of  which  is  a  inches 
is,  therefore,  given  by  the  following  formula,  due  to  Dawes : 

Formula  for 

f/n  —      *  -  diameter  of 

a  spurious 

disk. 
If  the  magnifying  power  is  too  great  (more  than  about  sixty 

to  the  inch  of  aperture),  the  disk  of  a  star  will  become  ill-defined 
at  the  edge ;  so  that  there  is  very  little  use  with  most  objects  in 
pushing  the  magnifying  power  any  higher. 

This  effect  of  "diffraction"  has  much  to  do  with  the  supe- 
riority of   large    instruments    in   showing  minute   details;   no 
increase  of  magnifying  power  on  a  small  telescope  can  exhibit  Superiority 
the  object  as  sharply  as  the  same  power  on  a  large  one,  pro-  c 
vided,  of  course,  that  the  object-glasses  are  equally  good  in  work-  glasses  in 
manship  and  that  the  atmospheric  conditions  are  satisfactory,  defining 

DOW6T» 

(But  a  given  amount  of  atmospheric  disturbance  injures  the  per- 
formance of  a  large  telescope  much  more  than  that  of  a  small  one.) 

47.  Eyepieces,  or  "  Oculars. "  —  For  some  purposes  the  simple 
convex  lens  is  the  best  eyepiece  possible  ;  but  it  performs  well 
only  for  a  small  object,  like  a  close  double  star,  exactly  in  the 
center  of  the  field  of  view.  Generally,  therefore,  we  employ 
eyepieces  composed  of  two  or  more  lenses,  which  give  a  larger 
field  of  view  than  a  single  lens  and  define  fairly  well  over  the 
whole  extent  of  the  field.  They  fall  into  two  general  classes, 
the  positive  arid  the  negative. 

The  positive  eyepieces  are  much  more  generally  useful.     They  Positive 
act  as  simple  magnifying-glasses  and  can  be  taken  out  of  the  eyePieces- 
telescope  and  used  as  hand  magnifiers  if  desired.     The  image  of 
the  object  formed  by  the  object-glass  lies  outside  of  this  kind 
of  eyepiece,  between  it  and  the  object-glass. 

In  the  negative  eyepieces,  on  the  other  hand,  the  rays  from  Negative 
the  object  are  intercepted  by  the  so-called  "  field  lens  "  before  eyePleces- 


38  MANUAL   OF   ASTRONOMY 

reaching  the  focus,  and  the  image   is  formed  inside   the  eye- 
piece.    It  cannot  therefore  be  used  as  a  hand  magnifier. 

Fig.  14  shows  the  two  most  usual  forms  of  eyepiece,  and 
also  the  "  solid  eyepiece  "  constructed  by  Steinheil ;  but  there 
are  a  multitude  of  various  kinds.  All  these  eyepieces  show 
the  object  inverted,  which  is  of  no  importance  in  astronomical 
observations. 


Steinheil  'Monocentric' 
(Positive) 


Huyghenian 
(Negative) 


FIG.  14.  —  Various  Forms  of  Telescope  Eyepiece 

It  is  evident  that  in  an  achromatic  telescope  the  objec1>glass  is  by  far 
the  most  important  and  expensive  member  of  the  instrument.  It  costs, 
according  to  size,  from  $100  up  to  $65000,  while  the  eyepieces  cost  only 
from  $2  to  $25  apiece,  and  every  telescope  of  any  pretension  possesses  a 
considerable  stock,  of  various  magnifying  powers. 

48.  Reticle.  —  If  the  telescope  is  to  be  used  for  pointing 
The  reticle,  upon  an  object,  it  must  be  provided  with  a  "  reticle"  of  some 
sort.  The  simplest  is  a  frame  with  two  spider-lines  stretched 
across  it  at  right  angles  to  each  other,  their  intersection  being 
the  point  of  reference.  This  reticle  is  placed,  not  at  or  near 
the  object-glass,  as  often  supposed,  but  in  the  focal  plane,  as 
ab  in  Fig.  12  (Sec.  41).  Of  course,  positive  eyepieces  only  can 
be  used  in  connection  with  such  a  reticle,  though  in  sextant 
telescopes  a  negative  eyepiece  is  sometimes  used  with  a  pair 
of  cross-wires  placed  between  the  two  lenses  of  the  eyepiece. 
Sometimes  a  glass  plate  with  fine  lines  ruled  upon  it  is  used 
instead  of  spider-lines.  In  order  to  make  the  lines  of  the 


ASTRONOMICAL   INSTRUMENTS  39 

reticle  visible  at  night,  a  faint  light  is  reflected  into  the  instru- 
ment by  some  one  of  various  arrangements  devised  for  the 
purpose. 

49.   The  Reflecting  Telescope.  —  About  16 TO,  when  the  chro-  Thereflect- 

matic  aberration  of  refractors  first  came  to  be  understood  (in  mstele~ 

x        scope. 

consequence  of  Newton's  discovery  of  the  decomposition  of 
light),  the  reflecting  telescope  was  invented.  For  nearly  one 
hundred  and  fifty  years  it  held  its  place  as  the  chief  instru- 
ment for  star-gazing.  There  are  several  varieties,  differing  in 
the  way  in  which  the  image  formed  by  the  mirror  is  brought 

Gregorian 


Cassegrainian 


Newtonian 
FIG.  15.  — Reflecting  Telescopes 

within  reach  of  the  magnifying  eyepiece.     Fig.  15  illustrates 

three   of  the   most  common  forms.     The   Newtonian   is   most  Various 

used,  but  one  t)r  two  large  instruments  are  of  the  Cassegrainian  forms  of  the 

form,  which  is  exactly  like  the  Gregorian  shown  in  the  figure 

(now  almost  obsolete),  with  the  exception  that  the  small  mirror 

is  convex  instead  of  concave. 

In  the  Herschelian,  or  "front  view"  form,  the  large  mirror 
is  slightly  inclined,  throwing  the  rays  to  the  edge  of  the  open 
end  of  the  tube,  so  that  the  secondary  mirror  is  dispensed  with, 
and  the  observer  stands  with  his  back  to  the  object.  This  is 
practicable  only  with  very  large  instruments,  since  the  head 


40 


MANUAL   OF   ASTRONOMY 


Mirrors  of 
silver  on 
glass. 


Superiority 
of  the 
refracting 
telescope 
over  the 
reflecting. 


Certain 
advantages 
of  the 
reflector. 


Large 
refractors 


of  the  observer  partly  obstructs  the  light;  the  image  also  is 
somewhat  distorted,  and  at  present  this  construction  is  never 
used. 

Until  about  1870,  the  large  mirror  (technically  speculum) 
was  always  made  of  speculum-metal,  a  composition  of  copper 
and  tin.  It  is  now  usually  made  of  glass,  silvered  on  the  front 
surface  by  a  chemical  process.  When  new,  these  silvered  films 
reflect  much  more  light  than  the  old  speculum-metal ;  they  tar- 
nish rather  easily,  but  fortunately  can  be  easily  renewed. 

50.  Relative  Advantages  of  Reflectors  and  Refractors. — There 
is  much  earnest  discussion  on  this  point,  each  form  of  instru- 
ment having  its  earnest  partisans.     On  the  whole,  however, 
the  refractor  is  usually  better.     Up  to  a  certain  limit,  never 
yet  reached,  it  gives  more  light  than  a  reflector  of  the  same 
size,  defines  better  under  all  ordinary  conditions,  has  a  wider 
field  of  view,  is  more  manageable  and  convenient,  and  more 
permanent;  the  speculum  of  a  reflector  usually  needs  to  be 
resilvered  every  few  years,  while  a  carefully  used  object-glass 
never  deteriorates. 

The  reflector  is  of  course  far  less  expensive  than  a  refractor 
of  the  same  size,  and  its  absolute  achromatism  is  a  great  advan- 
tage in  certain  lines  of  work,  photographic  and  spectroscopic. 

For  a  fuller  discussion  of  the  matter,  see  General  Astronomy. 

51.  Large  Telescopes.  —  The  largest  refractors1  at  preseiit*(1909)  exist- 
ing are  those  of  the  Yerkes  Observatory  (40  inches  in  diameter  and  65 
feet  long),    and    the  telescope  of   the  Lick  Observatory,  which   has    an 
aperture  of  36  inches  and  a  focal  length  of  56  feet.     There  are  about 
fourteen  others  which  have  apertures  not  less  than  2  feet.     The  object 
lenses  of   more   than  half  of  these  instruments,  including   both  of   the 
largest,  were  made  (that  is,  ground  and  figured)  in  this  country  by  the 
Clarks  of  Cambridgeport.     The  glass  itself  was  made  by  various  firms 
in  Europe. 

1  No  account  is  taken  in  this  reckoning  of  the  great  48-inch  telescope  of  the 
Paris  Exposition.  It  is  not  certain  as  yet  how  it  will  turn  out  from  an  astro- 
nomical point  of  view. 


ASTRONOMICAL   INSTRUMENTS 


41 


The  frontispiece  is  the  great  Potsdam  double  telescope,  —  two  mounted 
together,  —  one  31^  inches  in  diameter  for  photography,  the  other  20  inches 
in  diameter  for  visual  observations ;  the  focal  length  of  both  is  about  43 
feet.  It  was  erected  in  1899. 

At  the  head  of  the  reflectors  stands  the  enormous  instrument  of  Lord 
Rosse  of   Birr  Castle,   6  feet   in    diameter   and   60   feet  long,  made   in 
1842,  and  still  used  occasionally.    One  still  larger,  100  inches  in  diameter,   Large 
is   planned   for  the   Carnegie   Solar  Observatory  on   Mt.  Wilson,   where  reflectors, 
a  5-foot  reflector  was  mounted  in  1908.    Another  5-foot  reflector1  was 
made   by  Mr.  Common   in  England   in  1889.     There   are  also  four  or 
five  4 -foot  telescopes,  of  which  Herschel's 
(erected  in  1789,  but  long  ago  dismantled) 
was  the  first. 

At  the  Lick  Observatory  is  the  3-foot  in- 
strument (made  by  Mr.  Common  and  pre- 
sented to  the  observatory  by  Mr.  Crossley) 
with  which  Keeler  made  his  wonderful  pho- 
tographs of  nebulae,  some  of  which  are  figured  <&<y  //^  )  )  ^\  s>  C 
in  the  last  chapter  of  this  book.  Another  of 
2 -foot  aperture  is  mounted  at  the  Yerkes 
Observatory,  and  there  is  a  new  40-inch  in- 
strument at  Flagstaff,  Arizona. 

52.   Mounting  of  a  Telescope.  —  A 

telescope,  however  excellent  optically, 
is  of  little  scientific  use  unless  firmly 
and  conveniently  mounted.2 

At   present    nearly   all    but    small 
portable  instruments  are  mounted  as  Equatorial*. 
resents  the  arrangement  schematically.     Its  essential  feature  is 
that  the  "principal  axis"  —  the  one  which  moves  in  fixed  bear- 
ings attached  to  the  pier  and  is  called  the  polar  axis  —  is  inclined 
so  as  to  point  towards  the  celestial  pole.     The  graduated  circle 
H  attached  to  it  is  therefore  parallel  to  the  celestial  equator, 


FIG.  16.  — The  Equatorial 
(Schematic) 


The 


•IT,.       w  r>  equatorial 

Fig.  16  rep-  £oimting. 


1  Acquired  and  mounted  at  the  Harvard  College  Observatory  in  1905. 

2  We  may  add  that  it  must  be  mounted  where  it  can  be  pointed  directly  at 
the  stars,  without  any  intervening  window-glass  between  it  and  the  object. 


42 


MANUAL   OF   ASTRONOMY 


Advantages 
of  equa- 
torial 
mounting. 

Permits  use 
of  clock- 
work. 


Makes  it 
easy  to  find 
objects  too 
faint  to  be 


Use  of 
equatorial 
in  determin- 
ing position 
of  planets  or 
qpmets. 


and  is  usually  called  the  hour-circle  of  the  instrument,  — 
sometimes  the  right-ascension  circle.  At  the  upper  extremity 
of  the  polar  axis  a  sleeve  is  fastened,  which  carries  the 
declination  axis  D  passing  through  it.  To  one  end  of  this 
declination  axis  is  attached  the  telescope  tube  T,  and  at  the 
other  end  the  declination  circle  (7,  and  a  counterpoise  if 
necessary. 

53.  The  advantages  of  the  equatorial  mounting  are  very 
great.  In  the  first  place,  when  the  telescope  is  once  pointed 
upon  an  object  it  is  not  necessary  to  turn  the  declination 
axis  at  all  in  order  to  keep  the  object  in  view,  but  only  to 
turn  the  polar  axis  with  a  perfectly  uniform  motion,  which 
can  be,  and  usually  is,  given  by  clockwork  (not  shown  in  the 
figure). 

In  the  next  place,  it  is  very  easy  to  find  an  object,  even  if 
invisible  to  the  eye  (like  a  faint  comet,  or  a  star  in  the  day- 
time), provided  we  know  its  right  ascension  and  declination 
and  have  the  sidereal  time,  —  a  sidereal  clock  or  chronometer 
being  an  indispensable  accessory  of  the  equatorial.  We  set 
the  declination  circle  by  its  vernier  to  the  declination  of  the 
object  and  then  turn  the  polar  axis  until  the  hour-circle  shows 
the  proper  hour  angle,  which  is  simply  the  difference  between 
the  right  ascension  of  the  object  and  the  sidereal  time  at  the 
moment.  When  the  telescope  has  been  so  set  the  object  will 
be  found  in  the  field  of  view,  provided  a  low-power  eyepiece  is 
used.  On  account  of  refraction  the  setting  does  not  direct 
the  instrument  precisely  to  the  apparent  place  of  the  object, 
but  only  very  near  it. 

The  equatorial  does  not  give  very  accurate  positions  of 
heavenly  bodies  by  means  of  the  direct  readings  of  its  circles, 
but  it  can  be  used  as  explained  later  in  Sec.  117  to  determine 
with  great  precision  the  difference  between  the  position  of  a 
known  star  and  that  of  a  comet  or  planet;  and  this  answers 
the  purpose  as  well  as  a  direct  determination. 


ASTRONOMICAL   INSTRUMENTS 


43 


The  frontispiece  shows  the  equatorial  mounting  of  the  great  Potsdam  tel- 
escope. Fig.  173  (Sec.  536)  represents  another  form  of  equatorial  mounting, 
adopted  for  several  of  the  instruments  of  the  photographic  campaign.  Lord 
Rosse's  great  reflector  is  not  mounted  equatorially,  nor  was  HerschePs  4-foot 
reflector,  but  nearly  all  the  other  reflectors  referred  to  above  are  equatorials. 

54.  Other  Mountings.  —  With  very  large  telescopes  this 
mounting  becomes  unwieldy,  notwithstanding  the  ingenious 
electrical  and  other  arrangements  by  which  the  observer  at 


FIG.  17.  —The  Equatorial  Coude 

the  eyepiece  is  enabled  to  control  its  motions.  The  enor- 
mous rotating  dome  —  that  of  the  Yerkes  Observatory  is  90 
feet  in  diameter — and  the  requisite  elevating  floor  are  also 
extremely  expensive,  so  that  at  present  there  is  among  astron- 
omers a  tendency  to  adopt  plans  by  which  the  telescope  may 
be  fixed  in  its  position,  while  the  light  is  brought  to  the  eye- 
piece by  one  or  more  reflections  from  plane  mirrors. 

Fig.  17  represents   the  smaller  equatorial  coude,  or  "elbowed  equato- 
rial," of  the  Paris  Observatory.     A  silvered  mirror  at  an  angle  of  45°  in 


44 


MANUAL   OF   ASTRONOMY 


The 

equatorial 

coude. 


Importance 

of  Huy- 

ghens' 

invention 

of  the 

pendulum 

clock. 


the  box  in  front  of  the  object-glass,  and  another  one  in  the  cube  at  the 
center  of  the  instrument,  effect  the  necessary  changes  in  the  direction  of  the 
ray.  The  observer  sits  motionless,  under  cover,  at  the  eyepiece,  looking 
downward  towards  the  south,  at  an  angle  equal  to  the  latitude  of  the  place. 
A  much  larger,  similar  instrument,  since  mounted  at  the  same  observatory, 
has  an  aperture  of  24  inches  and  a  focal  length  of  about  60  feet.  Three  or 
four  instruments  of  this  sort  are  now  in  use.1 

Another  arrangement  is  to  place  the  telescope  horizontally,  pointing 
towards  the  south,  and  to  direct  the  light  from  the  object  into  it  by 
reflection  from  the  mirror  of  a  so-called  siderostat  This  is  a  simple 
plane  mirror  larger  than  the  object-glass,  properly  mounted  and  driven 
by  clockwork  so  as  to  send  the  reflected  rays  horizontally  always  in  the 
same  direction,  and  having  connections  by  which  its  motions  can  be  con- 
trolled from  the  eye  end  of  the  telescope.  The  great  telescope  of  the  Paris 
Exposition  of  1900  was  arranged  in  this  way. 

The  ccelostat  is  a  slightly  different  arrangement,  in  which  the  plane 
mirror,  mounted  upon  a  polar  axis,  revolves  at  half  the  diurnal  rate,  and 
the  telescope,  while  retaining  one  fixed  position  for  a  body  in  a  given 
declination,  has  to  change  its  position  to  observe  bodies  in  a  different 
declination.  There  are  still  other  forms  in  which  a  large  reflector  is  used 
to  give  the  rays  a  convenient  direction. 

But  the  use  of  the  mirror  or  mirrors  involves  considerable  loss  of  light ; 
and  what  is  worse,  if  the  mirror  is  large  it  is  extremely  difficult  to  figure 
the  surface  with  the  requisite  accuracy,  and  to  prevent  slight  distortions 
by  variations  of  temperature  and  changes  of  position.  As  a  consequence, 
definition  is  seldom  as  satisfactory  as  with  telescopes  pointed  directlv  to 
the  heavens ;  still,  in  certain  operations  of  astronomical  photography,  the 
siderostat  and  coelostat  are  extremely  useful. 

55.  Timekeepers  and  Recorders.  —  Obviously  a  good  clock 
or  chronometer  is  an  essential  instrument  of  the  observatory. 
The  invention  of  the  pendulum  clock  by  Huyghens  in  1657 
was  almost  as  important  to  the  advancement  of  astronomy  as 
that  of  the  telescope  by  Galileo  ;  and  the  improvement  of  the 
clock  and  chronometer  through  the  invention  of  temperature 
compensation  by  Harrison  and  Graham  in  the  eighteenth  cen- 
tury is  fully  comparable  with  the  improvement  of  the  telescope 
by  the  achromatic  object-glass. 

1  See  Addendum  A,  at  beginning  of  book. 


ASTRONOMICAL   INSTRUMENTS 


45 


The  astronomical  clock  differs  from  any  other  clock  only  in  The  astro- 
being  made  with  extreme  care  and  in  having  a  pendulum  so  nom/cal 
constructed    that    its    rate   will    not    be   sensibly   affected    by 
changes  of  temperature.     The  mercurial  pen- 
dulum is  most  common,  but  other  forms  are 
also  used.     (See  Fig.  18.) 

The  pendulum  usually  beats  seconds  (rarely 
half  seconds),  and  the  clock  face  ordinarily  has 
its  second-hand,  minute-hand,  and  hour-hand 
each  moving  on  a  separate  center,  the  hour- 
hand  making  its  revolution  not  in  twelve 
hours,  as  in  an  ordinary  clock,  but  in  twenty- 
four,  the  hours  being  numbered  accordingly. 

In  cases  where  the  extremest  accuracy  of 
performance  is  required,  the  clock  is  placed 
in  an  underground  chamber,  where  the  tem- 
perature varies  only  slightly  or  not  at  all,  and 
is  besides  inclosed  in  an  air-tight  case,  within 
which  the  air  is  kept  at  a  uniform  pressure, 
since  changes  in  the  density  of  the  air  slightly 
affect  the  swing  of  the  pendulum.  Usually  a 
clock  loses  about  one  quarter  of  a  second  a 
day  for  a  rise  of  one  inch  in  the  barometer. 

Finally,  also,  the  astronomical  clock  is  usu- 
ally fitted  with  some  arrangement  for  making 
or  breaking  an  electric  circuit  at  every  second  or 
every  other  second,  so  that  its  beats  can  be  communicated  tele-  The  break- 
graphically  to  all  parts  of  the  observatory.  The  minute  is  usually  circult- 
marked  either  by  the  omission  of  a  second  or  by  a  double  tick. 

56.    Error  and  Rate.  —  The  error  or  correction  of  a  clock  is  the  Error  and 
amount  which  must  be  added  (algebraically)  to  its  face  indication  rate' 
to  give  the  true  time  ;  +  when  slow,  —  when  fast.     The  rate  is 
the   amount   it  loses   or  gains  daily  ;  +  when  losing,  —  when 
gaining.     Sometimes  the    hourly  rate  is  given  instead  of   the. 


FIG.  18 

Compensation  Pen- 
dulums 

I.  Graham's  Pendulum 
2.  Zinc-Steel  Pendulum 


46  MANUAL   OF   ASTRONOMY 

daily.  The  error  is  adjusted  by  simply  setting  the  hands ;  the 
rate  by  raising  or  lowering  the  pendulum  bob,  or  for  delicate 
final  adjustment  without  stopping  the  clock,  by  adding  or 
removing  small  pieces  of  metal  on  the  cover  of  the  cylindrical 
vessel  which  usually  constitutes  the  pendulum  bob. 

Perfection  in  an  astronomical  clock  consists  in  its  maintain- 
ing a  constant  rate,  i.e.,  in  gaining  or  losing  precisely  the  same 
amount  each  day;  for  convenience  the  rate  should  be  small, 
and  is  usually  kept  less  than  half  a  second  daily.  But  this  is 
a  mere  matter  of  adjustment. 

57.  The  Chronometer.  —  The  pendulum  clock  not  being  port- 
able, it  is  necessary  to  provide  timekeepers  that  are  so.     The 
chronometer  is  merely  a  carefully  made  watch  with  a  balance- 
wheel  compensated  to  run,  as  nearly  as  possible,  at  the  same 
rate  in  different  temperatures,  and  with  a  peculiar  escapement, 
which,  though  'unsuited  to  ordinary  usage,  gives  better  results 
than  any  other  when  treated  carefully. 

The  box  chronometer  used  on  shipboard  is  usually  about 
twice  the  diameter  of  a  common  pocket  watch,  and  is  mounted 
on  "  gimbals  "  so  as  to  remain  horizontal  at  all  times,  notwith- 
standing the  motion  of  the  vessel.  It  usually  beats  half  seconds. 

It  is  not  possible  to  secure  in  the  chronometer  balance  as 
perfect  a  temperature  correction  as  in  the  pendulum,  and  for 
this  and  other  reasons  the  best  chronometers  cannot  quite  com- 
pete with  the  best  clocks  in  precision;  but  they  are  sufficiently 
accurate  for  most  purposes,  and  of  course  are  vastly  more  con- 
venient for  field  operations,  while  at  sea  they  are  simply  indis- 
pensable. Never  turn  the  hands  of  a  chronometer  backward ;  it 
may  ruin  the  escapement. 

58.  Eye-and-Ear  Method  of  Observation.  —  The  old-fashioned 
method  of  time  observation  consisted  simply  in  noting  by  "  eye 
and  ear  "  the  moment  (in  seconds  and  tenths  of  a  second)  when 
the  phenomenon  occurred ;  as,  for  instance,  when  a  star  passed 
some  wire  of  the  reticle.     The  tenths,  of  course,  are  merely 


ASTRONOMICAL   INSTRUMENTS 


47 


estimated,  but  the  skilful  observer  seldom  errs  by  a  whole 
tenth  in  his  estimation.  Skill  and  accuracy  in  this  method  are 
acquired  only  by  long  practice. 

59.    Telegraphic    Method ;     the    Chronograph At    present  observation 

such  observations  are  usually  made  by  the  help  of  electricitv.  by  means  of 

J  J  J      thechrono- 


50s. 


x 


9  h.  35  m.  oo.o  s.        graph. 


FIG.  19.  —A  Chronograph  Record 


FIG.  20.  —  A  Chronograph 
By  Warner  &  Swasey 

The  clock  is  so  arranged  that  at  every  beat  (or  every  other 
beat)  of  the  pendulum  an  electric  circuit  is  made  or  broken 
for  an  instant,  and  this  causes  a  sudden  sideways  jerk  in  the 


48  MANUAL   OF   ASTRONOMY 

armature  of  an  electromagnet,  like  that  of  a  telegraph  sounder. 
This  armature  carries  a  fountain-pen,  which  writes  upon  a 
sheet  of  paper  wrapped  around  a  cylinder  six  or  seven  inches 
in  diameter,  which  cylinder  itself  is  turned  uniformly  by  clock- 
work once  a  minute  ;  at  the  same  time  the  pen  carriage  is  drawn 
slowly  along,  so  that  the  marks  on  the  paper  form  a  continuous 
helix,  graduated  into  second  or  two-second  spaces  by  the  clock 
beats.  When  taken  from  the  cylinder,  the  paper  presents  the 
appearance  of  an  ordinary  page  crossed  by  parallel  lines  spaced 
off  into  two-second  lengths,  as  shown  in  Fig.  19,  which  is  part 
of  an  actual  record. 

Fig.  20  represents  a  chronograph  of  the  usual  American  form. 

The  observer,  at  the  moment  when  a  star  crosses  the  wire, 
presses  a  "key"  which  he  holds  in  his  hand,  and  thus  inter- 
polates a  mark  of  his  own  among  the  clock  beats  on  the  sheet ; 
as,  for  instance,  at  X  and  Y  in  the  figure.  Since  the  beginning 
of  each  minute  is  indicated  on  the  sheet  in  some  way  by  the 
mechanism  which  produces  the  clock  beats,  it  is  very  easy  to 
read  the  time  of  X  and  Y  by  applying  a  suitable  scale,  the 
beginning  of  the  mark  made  by  the  key  being  the  moment  of 
observation. 

In  the  figure  the  initial  minute  marked  when  the  chronograph  was 
started  happened  to  be  9h35m,  the  zero  in  the  case  of  this  clock  being 
indicated  by  a  double  beat.  The  signal  at  X,  therefore,  was  made  at 
9h35m558.45,  and  that  of  Y  at  9h36m588.63.  The  "rattle"  just  pre- 
ceding X  was  the  signal  that  a  star  was  approaching  the  transit  wire. 

In  European  observatories  the  record  is  usually  made  by  a  more  simple 
but  less  convenient  apparatus  upon  a  long  fillet  or  ribbon  of  paper  drawn 
slowly  along.  At  a  few  observatories  in  this  country  a  more  complicated 
printing  chronograph,  invented  by  Professor  Hough  of  the  Dearborn  Observa- 
tory, is  used.  By  this  the  minutes,  seconds,  and  hundredths  of  a  second 
are  actually  printed  upon  the  fillet  in  type,'  like  the  record  of  sales  on  a 
stock  telegraph. 

60.  Meridian  Observations.  —  A  large  proportion  of  all  astro- 
nomical observations  for  determining  the  positions  of  the 


ASTRONOMICAL   INSTRUMENTS 


49 


heavenly  bodies  are  made  when  the  body  is  crossing  the  meridian 
or  is  very  near  it.  At  that  time  the  effects  of  refraction  and 
parallax  (to  be  discussed  later)  are  a  minimum,  and  as  they  act 
only  vertically  they  do  not  affect  the  time  when  a  body  crosses 
the  meridian  nor,  consequently,  its  observed  right  ascension. 
In  any  other  part  of  the  sky  both  these  coordinates  are  affected, 
and  the  calculation  of  the  correction  requires  the  computation  of 
the  uparallactic  angle"  in  the  astronomical  triangle  (Sec.  31). 

61.  The  transit-instrument  is  the  instrument  used  in  connec- 
tion with  a  sidereal  clock  or  chronometer,  and  often  with  a 
chronograph,  to  observe  the  time 
of  a  star's  transit,  or  passage  across 
the  meridian.  If  the  "  error  "  of 
the  sidereal  clock  at  the  moment 
is  known  and  allowed  for,  the 
corrected  time  of  the  observation 
will  be  the  right  ascension  of  the 
star  (Sec.  26). 

Vice  versa,  if  the  right  ascen- 
sion is  known,  the  error  of  the 
clock  will  be  the  difference  be- 
tween the  right  ascension  of  the 
object  and  the  time  observed. 

The  instrument  (Fig.  21)  con- 
sists essentially  of  a  telescope  carrying  at  the  eye  end  a  reticle 
and  mounted  on  a  stiff  axis  that  turns  in  V-shaped  bearings 
called  "Y's,"  which  can  have  their  position  adjusted  so  as  to 
make  the  axis  exactly  perpendicular  to  the  .meridian.  A 
delicate  spirit-level,  which  can  be  placed  upon  the  pivots  of 
the  axis  to  measure  any  slight  deviation  from  horizontality, 
is  an  essential  accessory  ;  and  it  is  practically  necessary  to 
have  a  small  graduated  circle  attached  to  the  instrument, 
in  order  to  set  it  at  the  proper  elevation  for  the  star  which  is 
to  be  observed. 


Advantage 
of  observa- 
tions on  the 
meridian. 


FIG.  21.  — The  Transit-Instrument 


The  transit- 
instrument. 


The  level, 
setting- 
circle,  and 
reversing 
apparatus. 


50 


MANUAL   OF   ASTRONOMY 


It  is  desirable,  also,  that  the  instrument  should  have  a 
reversing  apparatus  by  which  the  axis  may  be  easily  lifted  and 
safely  reversed  in  the  Y's  without  jar  or  shock. 

The  reticle  usually  contains  from  five  to  fifteen  "vertical 
wires "  crossed  by  two  horizontal  ones.  Fig.  22  shows  the 
reticle  of  a  small  transit  intended  for  observations  by  "  eye 
and  ear."  When  the  chronograph  is  to  be  used,  the  wires  are 
much  more  numerous  and  placed  nearer  together. 

In  order  to  make  the  wires  visible  at  night  the  field  must  be  illuminated. 
For  this  purpose  one  of  the  pivots  of  the  instrument  is  pierced  (some- 
times both  of  them),  so  that  the  light  from  a  lamp  will  shine  through  the 
axis  upon  a  small  reflector  placed  in  the  central 
cube  of  the  instrument,  where  the  axis  and  the 
tube  are  joined.  This  sends  sufficient  light 
towards  the  eye  to  illuminate  the  field,  while 
it  does  not  cut  off  any  considerable  portion  of 
the  rays  from  the  object. 


FIG.  22.  — Reticle  of  the 
Transit-Instrument 


The  observation  consists  in  noting 
the  instant,  as  shown  by  the  clock  or 
chronometer,  in  hours,  minutes,  seconds, 
and  tenths  of  a  second,  at  which  the 
star  crosses  each  wire  of  the  reticle. 

62.  The  instrument,  must  be  thoroughly  rigid,  without  any 
loose  joints  or  shakiness,  especially  in  the  mounting  of  the  object- 
glass  and  reticle.  Moreover,  the  two  pivots  should  be  of  the 
same  diameter,  accurately  round,  without  taper,  and  precisely 
in  line  with  each  other  ;  in  other  words,  they  must  be  portions 
of  one  and  the  same  geometrical  cylinder.  To  fulfil  this  condition 
taxes  the  highest  skill  of  the  mechanician. 

When  exactly  adjusted,  the  middle  wire  of  such  an  instru- 
ment always  precisely  coincides  with  the  meridian,  however 
the  instrument  may  be  turned  on  its  axis;  and  the  sidereal 
time  when  a  star  crosses  that  wire  is  therefore  the  star's  right 
ascension. 


ASTRONOMICAL  INSTRUMENTS 


51 


Another  form  of  the  instrument  now  much  used  is  often  called  the 
broken  transit,  of  which  Fig.  23  is  a  representation.  A  reflector  (usually 
a  right-angled  prism)  in  the  central  cube  of  the  instrument  directs  the 
rays  horizontally  through  one  end  of  the  axis  where  the  eyepiece  is 


FIG.  23.  —  A  Broken  Transit 
By  Warner  &  Swasey 

placed,  so  that  whatever  may  be  the  elevation  of  the  star  the  observer 
looks  straight  forward  horizontally,  without  needing  to  change  his  position. 
The  instrument  is  very  convenient,  but  is  usually  subject  to  rather  a  large 
error,  due  to  flexure  of  the  axis,  which,  even  if  it  exists,  produces  no  such 
effect  in  transits  of  ordinary  form.  The  error  is,  however,  easily  determined 
and  allowed  for  if  the  axis  is  not  too  slender. 


MANUAL   OF   ASTRONOMY 


Necessary 
adjust- 
ments. 


Tests  of 
adjust- 
ments. 


Non-perma- 
nence of 
adjust- 
ments. 


63.    Adjustments  of  the  Transit.  —  These  are  four  in  number-, 

(1)  The  reticle  must  be  exactly  in  the  focal  plane  of  the 
object-glass  and  the  middle  wire  accurately  vertical. 

(2)  The  line  of  collimation  (i.e.,  the  line  which  joins  the  optical 
center  of  the  object-glass  to  the  middle  wire)  must  be  exactly 
perpendicular  to  the  axis  of  rotation.     This  may  be  tested  by 
pointing  on  a  distant  mark  and  then  reversing  the  instrument. 
The  middle  wire  must  still  bisect  the  mark  after  the  reversal. 
If  not,  the  reticle  must  be  adjusted  by  the  screws  provided  for 
the  purpose. 

(3)  The  axis  must  be  level.    This  adjustment  is  made  mechan- 
ically by  the  help  of  the  spirit-level.     One  of  the  Y's  has  a 
screw  by  which  it  can  be  slightly  raised  or  lowered,  as  may  be 
necessary. 

(4)  The  azimuth  of  the  axis  must  be  exactly  90° ;   i.e.,  the 
axis  must  point  exactly  east  and  west.      This  adjustment  is 
made  by  means  of  star  observations,  with  the  help  of  the  side- 
real clock. 

Without  going  into  detail,  we  may  say  that  if  the  instrument 
is  correctly  adjusted,  the  time  occupied  by  a  star  near  the  pole, 
in  passing  from  its  transit  across  the  middle  wire  above  the 
pole  to  its  next  transit  below  the  pole,  must  be  exactly  twelve 
sidereal  hours.  Moreover,  if  two  stars  are  observed,  one  near 
the  pole  and  another  near  the  equator,  the  difference  between 
their  times  of  transit  ought  to  be  precisely  equal  to  their  differ- 
ence of  right  ascension.  By  utilizing  these  principles  the 
astronomer  can  determine  the  error  of  azimuth  adjustment  and 
correct  it. 

But  it  is  to  be  remembered  that  no  adjustments,  however 
carefully  made,  will  be  absolutely  exact  or  remain  permanently 
correct,  on  account  of  changes  in  temperature  which  affect  the 
instrument  and  the  pier  on  which  it  is  mounted.  In  cases 
where  extreme  accuracy  of  results  is  required,  the  slight  errors 
which  remain  after  the  most  careful  adjustment  must  be 


ASTRONOMICAL   INSTRUMENTS  53 

determined  from  the  observations  themselves  by  means  of  the 
little  discrepancies  between  the  results  obtained  from  stars  at 
different  distances  from  the  pole.  The  methods  to  be  used  are 
taught  in  practical  astronomy. 

64.   Personal  Equation.  —  It  is  found  that  skilled  observers  Personal 
are  in  the  habit  of  noting  the  passage  of  a  star  across  the  e(iuatlon- 
transit  wire  slightly  too  late  or  too  early  by  an  amount  which 
is  different  for  each  observer,  but  nearly  constant  for  each. 
This  is  called  the   observer's  personal  equation,  and  in  some 
cases  for  eye-and-ear  observation  is  as  much  as  half  a  second, 
In  the  telegraphic  method  it  is  much  less,  seldom  exceeding 
Os..l.     It  is  an  extremely  troublesome  error,  because  it  varies 
with  the  nature   and   brightness  of   the  object  and  with  the 
observer's  position  and  physical  condition. 

Various  devices  have  been  proposed  for  dealing  with  it  ;  either  by   Mechanical 
measuring  its  amount,  or  by  eliminating  it  by  means  of  some  apparatus   method  of 


which  reduces  the  observation  to  the  accurate  bisection  of  the  star  disk,   ^e   m^  ri 
made  to  appear  to  be  at  rest  by  a  clockwork  motion  given  to  the  eyepiece,    equation 
and  carrying  with  it  a  "  micrometer  wire  "  which  is  under  the  control  of 
the  observer.     When  the  bisection  is  satisfactory  he  touches  a  key  which 
instantly  stops  the  motion  and  registers  the  time  upon  the  chronograph  ; 
afterwards,  at  his  leisure,  he  measures  the  distance  of  his  micrometer  wire 
from  the  central  wire  of  the  reticle.     In  this  way  the  disturbing  effect  of 
the  star's  motion  is  eliminated. 

65.   The  Photochronograph.  —  Another  method,  and  one  of  the  most   Photo- 
promising,  is  by  means  of  photography.      The  eyepiece  of  the  transit  is   graphic 
removed,  and  a  small  photographic  plate,  about  as  large  as  a  microscope   °  sei 
slide,  is  placed  just  back  of  the  reticle,  so  arranged  in  the  frame  which 
holds  it  that  it  can  move  up  and  down  slightly  under  the  action  of  an 
electromagnet  connected  with  the  standard-clock  circuit.      When  a  star 
impresses  its  "trail"  on  the  plate,  the  trail  is  broken  every  second  (or 
every  other  second)  by  the  clock,  like  the  marks  on  a  chronograph  sheet, 
so  that  it  consists  of  a  row  of  small  dashes.     The  image  of  the  reticle 
wires  is  also  imprinted  upon  the  plate  by  holding  a  small  lamp  for  an 
instant  in  front  of  the  object-glass. 

During  the  passage  of  the  star  some  particular  second  is  marked  on 
the  plate  by  cutting  off  the  clock  circuit  for  two  or  three  seconds,  or  by 


54 


MANUAL   OF   ASTRONOMY 


The  prime 

vertical 

instrument. 


Its  use. 


The  almu- 
cantar  and 
its  use. 


making  a  rattle,  allowing  the  beats  to  resume  their  regular  course  at  some 
instant  recorded  in  the  note-book.  After  the  plate  is  developed,  its  inspec- 
tion and  measurement  under  a  microscope  will  show  at  what  second  and 
fraction  of  a  second  the  star  passed  each  reticle  wire.  But  this  part  of  the 
operation  is  laborious.  On  the  other  hand,  the  expensive  and  troublesome 
chronograph  is  dispensed  with. 

66.  The  Prime  Vertical  Instrument.  —  For  certain  purposes 
a   transit-instrument,    provided   with   an    apparatus   for   rapid 
reversal,  is  turned  quarter  way  round  and  mounted  with  its 
axis  north  and  south,  so  that  the  plane  of  rotation  lies  east  and 
west  instead  of  in  the  meridian.     It  is  then  called  the  "  prime 
vertical  instrument."     It  may  be  used  for  determining  the  lati- 
tude of  the  observer,  the  precise  declination  of  such  stars  as 
cross  the  meridian  between  the  zenith  and  equator,  and  any 
minute  change  due  to  "aberration"  and  to  slight  movements 
of  the  terrestrial  pole.     (See  Sec.  94.) 

The  observation  consists  in  noting  the  instant  when  the  star 
crosses  (obliquely)  the  middle  wire  of  the  reticle. 

67.  The  Almucantar.  —  This  is  an  instrument  invented  about 
1885  by  Dr.  S.  C.  Chandler  of  Cambridge,  U.S.,  for  the  pur- 
pose of  observing  the  time  at  which  stars  cross,  not  the  meridian 
or  any  vertical  circle,  but  some  given  parallel  of  altitude,  usually 
the  "  almucantar  "  of  the  pole.     From  such  observations  can  be 
determined  with  great  accuracy  the  error  of  the  clock,  the  decli- 
nation of  the  stars  observed,  or  the  latitude  of  the  observer. 

It  consists  of  a  firm  base  carrying  a  tank  containing  mercury, 
on  which  swims  a  float  which  carries  the  observing  telescope, 
its  inclination  being  preserved  absolutely  constant  by  the  prin- 
ciple of  flotation.  This  dispenses  with  the  necessity  of  using 
spirit-levels  (which  are  always  more  or  less  unsatisfactory)  for 
determining  the  inclination. 

The  telescope  is  sometimes  placed  horizontally  on  the  float,  while  a  mirror 
in  front  of  its  object-glass  brings  down  the  rays  of  the  star.  Two  such 
instruments  of  considerable  size  have  been  built  since  1899  and  give  prom- 
ising results, —  one  at  Durham,  England,  the  other  at  Cleveland,  Ohio. 


ASTRONOMICAL   INSTRUMENTS 


55 


68.    The    Meridian-Circle This  is  a  transit-instrument  of  The  merid- 

large  size  and  most  careful  construction,  with  the  addition  of  a  ian~circle : 

essentials  of 

large  graduated  circle  attached  to  the  axis  and  turning  with  it.  its  construc- 
tion. 


FIG.  24.  —Meridian-Circle  in  United  States  Naval  Observatory,  Washington 
By  Warner  &  Swasey 

The  utmost  resources  of  mechanical  art  are  expended  in  gradu- 
ating this  circle  with  precision.  The  divisions  are  now  usually 
made  either  two  minutes  or  five  minutes  of  arc,  and  the  farther 


56 


MANUAL   OF   ASTRONOMY 


Its  zero 
points. 


Determina- 
tion of  the 
polar  point. 


Determina- 
tion of  the 
nadir  point. 


subdivision  is  effected  by  so-called  "reading  microscopes," 
four  of  which  at  least  are  always  used  in  the  case  of  a  large 
instrument.  (For  a  description  of  the  reading  microscope,  the 
reader  is  referred  to  Creneral  Astronomy,  Art.  64,  or  to  Camp- 
bell's Practical  Astronomy.)  By  means  of  these  microscopes 
the  "reading  of  the  circle"  is  made  in  degrees,  minutes,  sec- 
onds, and  tenths  of  a  second  of  arc,  the  tenths  being  obtained 
by  estimation. 

On  a  circle  2  feet  in  diameter  1"  of  arc  is  only  about  T7^  part  of 
an  inch  ;  an  error  of  that  amount  is  now  very  seldom  made  by  reputable 
constructors  in  placing  a  graduation  line,  or  by  a  good  observer  in  reading 
the  instrument  with  the  microscope. 

Fig.  24  represents  the  new  meridian-circle  of  the  United  States  Naval 
Observatory  at  Washington,  with  a  6-inch  telescope  and  circles  about 
27  inches  in  diameter. 

69.  Zero  Points.  —  The  instrument  is  used  to  measure  the 
altitude  or  else  the  polar  distance  of  a  heavenly  body  at  the 
time  when  it  is  .crossing  the  meridian.  As  a  preliminary  we 
must  determine  some  zero  point  upon  the  circle,  —  the  nadir 
point  or  horizontal  point,  if  we  wish  to  measure  altitudes  or 
zenith-distances  ;  the  polar  point  or  equator  point,  if  polar  dis- 
tances or  declinations.  The  polar  point  is  determined  by  taking 
the  circle  reading  for  some  star  near  the  pole  when  it  crosses 
the  meridian  above  the  pole,  and  then  doing  the  same  thing 
again  twelve  hours  later  when  it  crosses  it  below.  The  mean 
of  the  two  readings  corrected  for  refraction  will  be  the  reading 
which  the  circle  would  give  when  the  telescope  is  pointed 
exactly  to  the  pole, — technically,  the  polar  point.  The  equator 
point  is,  of  course,  90°  from  this. 

The  nadir  point  is  the  reading  of  the  circle  when  the  tele- 
scope is  pointed  vertically  downward.  It  is  determined  by  the 
reading  of  the  circle  when  the  instrument  is  so  set  that  the 
horizontal  wire  of  the  reticle  coincides  with  its  own  image 
formed  by  a  reflection  from  a  basin  of  mercury  placed  on  the 


ASTRONOMICAL   INSTRUMENTS 


57 


pier   below   the   instrument.     To   make   this   reflected   image 
visible  it  is  necessary  to  illuminate  the  reticle  by  light  thrown 
towards  the  object-glass  from  behind  the  wires,  —  the  ordinary  The  colii 
illuminatiori  used  during  observation  comes  from  the  opposite 
direction.      This  peculiar  illumination  is  effected  by  what  is 
known  as  the  "collimating  eye- 
piece." A  thin  glass  plate  inserted 
at  an  angle  of  45°  between  the 
lenses    of    a    Ramsden   eyepiece 
throws  down  sufficient  light,  ad- 
mitted through  a  hole  in  the  side 
of  the  eyepiece,  and  yet  permits 
the  observer  to  see  the  wires  and 
their  reflected  image.    The  zenith 
point  is,  of  course,  just  180°  from 
the  nadir  point  thus  determined. 

Obviously,  the  meridian-circle  can 
be  used  simply  as  a  transit,  so  that  with 
this  instrument  and  a  clock  the  observer 
is  in  a  position  to  determine  both  the 
right  ascension  and  declination  of  any 
heavenly  body  that  can  be  seen  when 
it  crosses  the  meridian. 


FIG.  25.  —  A  5-inch  Altazimuth 
By  Warner  &  Swasey 


Extra- 
meridian 
observa- 
tions. 


70.    Extra-Meridian  Observa- 
tions. —  Many  objects,  however, 
are  not  visible  when  they  cross 
the   meridian;    a  comet,   for   in- 
stance,  or  a  planet,   may  be   in 
such  a  part  of  the  heavens  that  it  transits  only  by  daylight.    To 
observe  such  objects  we  may  employ  a  so-called  universal  instru- 
ment, or  astronomical  theodolite,  which  is   simply  an  instru-  Theuniver- 
ment  with  both   horizontal  and  vertical  circles  like    a   large  salmstrn- 

ment,  or 

surveyor's  theodolite  and  is  also  called  an  altazimuth.    By  means  altazimuth 
of  this  the  altitude  and  azimuth  of  an  object  may  be  measured, 


58 


MANUAL   OF   ASTRONOMY 


Extra- 
meridian 
observa- 
tions with 
the  equa- 
torial. 


and,  if  the  time  is  given,  from  these  the  right  ascension  and 
declination  can  be  deduced. 

Fig.  25  shows  the  5-inch  altazimuth  of  the  Washington  Observatory. 

More  often,  however,  observations  for  the  positions  of  bodies 
not  on  the  meridian  are  made  with  the  equatorial  telescope 

already  described,  with  which 
the  difference  between  the  right 
ascension  and  declination  of 
the  observed  body  and  that 
of  some  star  in  its  neighbor- 
hood is  determined  by  means 
of  a  micrometer  or,  at  present, 
often  by  photography. 

71.    The    Micrometer. - 
There    are    various    forms    of 
micrometers,  the  most  common 
and  generally  useful  being  that 

(A)  r^QBJ — — ^lyilpW    known  as  the  filar-position  mi- 

crometer, shown  in  Figs.  26  A 


FIG.  26.  —  The  Filar-Position  Micrometer 


and  B.  It  is  a  comparatively  small  instrument  which  is  attached 
at  the  eye  end  of  the  telescope.  It  usually  contains  a  set  of  fixed 
wires,  two  or  three  of  them  parallel  to  each  other  (only  one,  e, 
is  shown  in  B,  which  represents  the  internal  construction 


ASTRONOMICAL   INSTRUMENTS 


59 


of  the  instrument),  crossed  at  right  angles  by  a  single  line  or 
set  of  lines.  Under  the  plate  which  carries  the  fixed  threads 
lies  a  fork  moved  by  a  carefully  made  screw  with  a  graduated 
head,  and  this  fork  carries  one  or  more  wires  parallel  to  the  first 
set,  so  that  the  distance  between  the  wires  e  and  d  (Fig.  26  B) 
can  be  varied  at  pleasure  and  read  off  by  means  of  the  screw- 
head  graduation. 

The  box  containing  the  wires  is  so  arranged  that  it  can  itself 
be  rotated  around  the  op- 
tical axis  of  the  telescope 
and  set  in  any  desired 
"  position  "  ;  for  example, 
so  that  the  movable  wire 
d  shall  be  parallel  to  the 
celestial  equator  when  the 
position  circle  F  should 
read  90°.  When  so  set  that 
the  movable  wire  points 
from  one  star  to  another  in 
the  field  of  view,  the  "  po- 
sition angle  "  (see  Fig.  191, 
Sec.  585)  can  be  read  off 
on  the  circle  F. 

With  such  a  micrometer 
we  can  measure  at  once  the 
distance  in  seconds  of  arc 
between  any  two  stars 
which  are  near  enough  to  be  distinctly  seen  in  the  same  field  of  its  use  and 
view,  and  can  determine  the  position  angle  of  the  line  joining 
them.     The  available  range  in  a  small  telescope  may  reach  30'. 
In  large  telescopes,  which  with  the  same  eyepieces  give  much 
higher  magnifying  powers,  the  range  is  correspondingly  less,  — 
not  more  than  from  5'  to  10'.     When  the  distance  between  the 
objects  exceeds  2'  or  3',  the  filar  micrometer  becomes  difficult 


FIG.  27.  —  Position  Micrometer 
By  Warner  &  Swasey 


60  MANUAL   OF   ASTRONOMY 

to  use  and  inaccurate,  because  the  observer  cannot  see  both 
objects  distinctly  at  the  same  time. 

Fig.  27  is  a  complete  micrometer,  fitted  with  electric  illumination. 

The  heiiom-        72.   The  Heliometer.  —  For  the  measurement  of  larger  dis- 
eter:itscon-  Dances  not  exceeding  two  or  three  degrees  the  heliometer  is  used. 
This   is   a  complete   equatorially   mounted  telescope   with  its 
object-glass  (usually  from  4  to  8  inches  aperture)  diametrically 
divided  into  two  halves  which  can  be  made  to  slide  past  each 
other  for  3  or  4  inches  (Fig.  28),  the  distance  being  measured 
on  a  delicate  scale  read  by  long  microscopes 
A\    Ao     A2          which  come  down  to  the  end  of  the  instru- 
x     ment.     The  telescope  tube  can  be  rotated 
j   in  its  cradle  so  as   to  make  the  line  of 
division  of  the  lenses  lie  in  any  desired 
position. 

When  the  objectrglass  scale  is  at  zero, 
MI    MO   Ma       the  two  half  lenses  act  as   a  single   lens 
^i    S0    S*  and  each  object  in  the  field  of  view  pre- 

sents   a   single    image,   as   Sn  and  Mn  in 

FIG.  28.  — The  Heliometer 

the  figure.  But  as  soon  as  one  of  the 

semi-lenses  is  pushed  past  the  other,  two  images  of  each 
object  appear,  and  the  distance  and  direction  between  them 
can  be  varied  at  pleasure  by  sliding  the  lenses  and  rotating 
the  tube. 

The  distance  between  any  two  different  objects  is  measured 
by  making  their  images  coincide  (as,  for  instance,  M±  with  $0,  or 
£2  with  MQ),  and  the  observer  does  not  have  to  "  look  two  ways 
at  once,"  nor  is  he  obliged  to  trust  to  the  stability  of  his  instru- 
ment or  the  accuracy  of  the  clockwork  motion. 

On  the  whole,  the  heliometer  stands  at  the  head  of  astro- 
nomical instruments  for  the  precision  of  its  results  and  is 
employed  in  the  most  delicate  investigations,  like  those  upon 
solar  and  stellar  parallax  (Sees.  467  and  550).  But  it  is  a 


ASTRONOMICAL   INSTRUMENTS  61 

very  complicated  and  costly  instrument,  and  extremely  laborious  The  rank 

to  «Se'  heHoLte, 

The  only  one  in  the  United  States  at  present  is  the  6-inch  among 

instrument  at  the  Yale  University  Observatory.  astronomi- 

At  present,  however,  such  measurements  of  the  distance  of  ments. 
an  object  from  neighboring  stars  are  very  generally  effected  by 

means  of  photography.     Photographs  of  the  field  of  view  con-  Observa- 

taininor  the  object  are  made  and  afterwards  measured,  and  in  tlonsby 

means  of 

this  case  the  limits  of  distance  between  the  object  and  the  stars  photog- 
to  which  it  is  referred   can  be  very  much  increased  without  raPhy- 
lessening  the  accuracy  of  the  determination. 

73.   The  Sextant. — All  the   instruments  so  far  mentioned,  The  sextant: 
except  the  chronometer,  require  some  firmly  fixed  support,  and  the  mstru~ 
are  therefore  absolutely  useless  at  sea.     The  sextant  is  the  only  mariner, 
one  upon  which  the  mariner  can  rely.     By  means  of  it  he  can 
measure    the    angular   distance    between    two   points    (as,    for 
instance,  between  the  sun  and  visible  horizon),  not  by  pointing 
first  to  one  and  afterwards  to  the  other,  but  by  sighting  them  its  peculiar 
both   simultaneously   and  in    apparent   coincidence,   a    "  double  advantage 
image  "  measurement,  in  which  respect  the  sextant  is  analo-  instruments, 
gous    to    the    heliometer.     A    skilful   observer  can  make    the 
measurement  accurately  even  when  he  has  no  stable  footing. 

Fig.  29  represents  the  instrument.  Its  graduated  limb  is 
usually,  as  its  name  implies,  about  a  sixth  of  a  complete  circle, 
with  a  radius  of  from  5  to  8  inches.  It  is  graduated  in  itscon- 
half  degrees  (which  are,  however,  numbered  as  whole  degrees)  structlon- 
and  so  can  measure  any  angle  not  much  exceeding  120°.  The 
index  arm,  or  "  alidade  "  (MN  in  the  figure),  is  pivoted  at  the 
center  of  the  arc  and  carries  a  "vernier,"  which  slides  along 
the  limb  and  can  be  fixed  at  any  point  by  a  clamp,  with  an 
attached  tangent  screw  T.  The  reading  of  this  vernier  gives 
the  angle  measured  by  the  instrument;  the  best  instruments 
read  to  10"  only,  because  it  is  impracticable  to  use  a  telescope 
with  very  much  magnifying  power. 


62 


MANUAL   OF   ASTRONOMY 


Just  over  the  center  of  the  arc  the  index-mirror  M,  about 
2  inches  by  li  in  size,  is  fastened  to  the  index  arm,  moving 
with  it  and  keeping  always  perpendicular  to  the  plane  of  the 
limb.  At  H  the  horizon-glass,  about  an  inch  wide  and  about 
twice  the  height  of  the  index-glass,  is  secured  to  the  frame  of 
the  instrument  in  such  a  position  that  when  the  vernier  reads 
zero  the  index-mirror  and  horizon-glass  will  be  parallel  to  each 


M 


IS' 


FIG.  29.  —  The  Sextant 

other.  Only  half  of  the  horizon-glass  is  silvered,  the  upper  half 
being  left  transparent.  E  is  a  small  telescope  screwed  to  the 
frame  and  directed  towards  the  horizon-glass. 

If  the  vernier  stands  near,  but  not  exactly  at,  zero,  an  observer 
looking  into  the  telescope  will  see  together  in  the  field  of  view 
two  separate  images  of  the  object  towards  which  the  telescope 
is  directed;  and  if  he  slides  the  vernier,  he  will  see  that  one  of 
the  images  remains  fixed  while  the  other  moves.  The  fixed 
image  is  formed  by  the  rays  which  reach  the  object-glass  directly 
through  the  unsilvered  half  of  the  horizon-glass ;  the  movable 


ASTRONOMICAL   INSTRUMENTS  63 

image,  on  the  other  hand,  is  produced  by  rays  which  have  Double 
suffered  two  reflections,  having  been  reflected  from  the  index-  ima&e 

&  formed  by 

mirror  to  the  horizon-glass  and  again  reflected  a  second  time  sextant, 
from  the  lower,  silvered  half  of  the  horizon-glass.     When  the 
two  mirrors  are  parallel  the  two  images  coincide,  provided  the 
object  is  at  a  considerable  distance. 

If  the  vernier  does  not  stand  at  or  near  zero,  an  observer  Angle 
looking  at  an  object  directly  through  the  horizon-glass  will  see 
not  only  that  object,  but  also,  in  the  same  telescopic  field  of  whose 
view,  whatever  other  object  is  so  situated  as  to  send  its  rays  imagescoin- 

.  .  ,         cide  equals 

to  the  telescope  by  reflection  from  the  mirrors ;  and  the  reading  half  the 
of  the  vernier  will  give  the  angle  at  the  instrument  between  the  two  ansle 
objects  whose   images   thus   coincide, — the    angles   between   the  mirrors 
planes  of  the  two  mirrors  being,  as  easily  proved,  just  half  the 
angle  between  the  two  objects,  and  the  half  degrees  on  the  limb 
being  numbered  as  whole  ones. 

74.    The  principal  use  of  the  instrument  is  in  measuring  the  altitude 
of  the  sun.     At  sea  the  observer  usually  proceeds  as  follows:  first,  setting   Method  of 
the  index,  loosely  clamped,  near  zero  and  holding  the  sextant  in  his  right   observation 
hand  with  its  plane  vertical,  he  points  the  telescope  towards  the  sun ;  then   at  sea" 
he  slides  the  vernier  along  the  arc  with  his  left  hand  until  he  brings  the 
reflected  image  of  the  sun  down  to  the  horizon,  all  the  time  keeping  it  in 
view  in  the  telescope;  finally,  tightening  the  clamp  and  using  the  tangent 
screw,  he  makes  the  lower  edge  or  limb  of  the  sun  just  graze  the  horizon 
as  he  swings  the  sun's  image  back  and  forth  by  a  slight  motion  of  the  instru- 
ment —  it  would  be  impossible  on  board  ship  to  hold  the  image  in  contact 
with  the  horizon,  and  is  not  necessary.     As  soon  as  the  contact  is  satis- 
factory he  marks  the  time  and  afterwards  reads  the  angle.     The  reading 
of  the  vernier  after  due  corrections  (see  next  chapter)  gives  the  sun's  true 
altitude  at  the  moment. 

On  land  we  have  recourse  to  an  "  artificial  horizon."     This  is  a  shallow  Artificial 
basin  of  mercury  covered  with  a  roof  of  glass  plates  having  their  surfaces   horizon  used 
accurately  plane  and  parallel.     In  this  case  we  measure  the  angle  between   ° 
the  sun  and  its  image  reflected  in  the  mercury.     The  reading  of  the  instru- 
ment corrected  for  index  error  then  gives  twice  the  sun's  apparent  altitude. 

The  skilful  use  of  the  sextant  requires  considerable  dexterity,  and  from 
the  low  power  of  the  telescope  the  angles  measured  are  less  precise  than 


64 


MANUAL   OF   ASTRONOMY 


those  determined  by  large  fixed  instruments,  but  the  portability  of  the 
instrument  and  its  applicability  at  sea  render  it  invaluable.  It  was 
invented  in  practical  form  by  Godfrey  of  Philadelphia,  in  1730,  though 
Newton,  as  was  discovered  by  Halley,  had  really  struck  upon  the  same 
idea  long  before. 

Demonstra-  75.  The  principle  that  the  angle  between  the  objects  whose  images 
tion  of  the  coincide  in  the  sextant  is  twice  the  angle  between  the  mirrors  (or  between 
^cTsextant  tne*r  normals)  is  easily  demonstrated  as  follows : 

The  ray  SM  (Fig.  30)  coming  from  an  object,  after  reflection  first  at  M 
(the  index-mirror)  and  then  at  H  (the  horizon-glass),  is  made  to  coincide 
with  the  ray  OH  coming  from  the  horizon. 

From  the  law  of  reflection,  we  have  the  two  angles  SMP  and  PMH 

equal  to  each  other,  each  being  x.  In  the 
same  way  the  two  angles  marked  y  are 
equal.  From  the  geometric  principle  that 
the  angle  SMH,  exterior  to  the  triangle 
HME,  is  equal  to  the  sum  of  the  oppo- 
site interior  angles  at  H  and  E,  we  get 
E  =  2  x  —  2  y.  Similarly,  from  the  tri- 
angle HM Q,  Q  =  x  -  y  ;  whence  E  =  2 
Q  =  2  Q'. 

76.    With  the  instruments  above 
described  all  the  fundamental  obser- 
vations required  in  the  investiga- 
tions of  spherical  and  theoretical 
astronomy  can  be  supplied,  the  sex- 
tant and  chronometer  being,  however,  the  only  ones  available 
in  nautical  astronomy. 

Astrophysical  studies  require  numerous  physical  instruments 
of  an  entirely  different  character,  —  spectroscopes,  photometers, 
heat-measuring  instruments,  and  various  kinds  of  photographic 
apparatus.  These  will  be  considered  later,  as  occasion  arises. 


FIG.  30.  —  Principle  of  the  Sextant 


ASTRONOMICAL   INSTRUMENTS  65 


EXERCISES 

1.  If  a  firefly  were  to  alight  on  the  object-glass  of  a  telescope,  what 
would  be  the  appearance  to  an  observer  looking  through  the  instrument  ? 
Would  he  think  he  saw  a  comet  ? 

2.  When  a  person  is  looking  through  a  telescope,  if  you  hold  your 
finger  in  front  of  the  object-glass,  will  he  see  it? 

t/   3.    If  half  the  object-glass  of  a  telescope  pointed  at  the  moon  is  covered, 
how  will  it  affect  the  appearance  of  the  moon  as  seen  by  the  observer  ? 
]/  4.    If  a  certain  eyepiece  gives  a  magnifying  power  of  60  when  used 
with  a  telescope  of  5  feet  focal  length,  what  power  will  it  give  on  a  tele- 
scope of  30  feet  focal  length  ? 

5.  What  is  theoretically  the  angular  distance  between  the  centers  of 
two  star  disks  which  are  just  barely  separated  by  a  telescope  of  24  inches 
aperture  (Sec.  46)  ? 

V    6.   Why  is  it  important  that  the  two  pivots  of   a  transit-instrument 
should  be  of  exactly  the  same  diameter? 

7.  If  the  wires  of  a  micrometer  (Fig.  26)  are  so  set  that,  used  with  a 
telescope  of  10  feet  focal  length,  a  star  moving  along  the  right-ascension 
wire  will  occupy  15  seconds  in  passing  from  d  to  e,  how  long  will  it  take 
when  the  micrometer  is  transferred  to  a  telescope  of  50  feet  focus  ? 

8.  If  the  threads  of  a  micrometer  screw  are  7V  of  an  inch  apart,  what 
is  the  angular  value  of  one  revolution  of  the  screw  when  the  micrometer 
is  attached  to  a  telescope  of  30  feet  focal  length  ? 

9.  Does  changing  the  eyepiece  of  a  telescope  for  the  purpose  of  altering 
the  magnifying  power  affect  the  value  of  the  revolution  of  the  microscope 
screw  V 


CHAPTER  III 


CORRECTIONS  TO  ASTRONOMICAL  OBSERVATIONS 

Dip  of  the  Horizon  —  Parallax—  Semidiameter  —  Refraction  —  Twinkling  or  Scintil- 

lation—Twilight 

OBSERVATIONS  as  actually  made  always  require  corrections 
before  they  can  be  used  in  deducing  results.  Those  that 
depend  on  the  errors  or  maladjustment  of  the  instrument  itself 
will  not  be  considered  here,  but  only  such  as  are  due  to  other 
causes  external  to  the  instrument  and  the  observer. 

77.  Dip  of  the  Horizon  --  In  observations  of  the  altitude  of  a 
heavenly  body  at  sea,  where  the  sextant  measurement  is  made 
from  the  visible  horizon,  or  sea-line,  it  is 
necessary  to  take  into  account  the  depres- 
sion of  the  visible  below  the  true  astro- 
nomical horizon  by  a  small  angle  called  the 
dip.  The  amount  of  this  dip  depends  upon 
the  observer's  altitude  above  the  sea-level. 
In  Fig.  31  C  is  the  center  of  the  earth, 
AB  a  portion  of  its  level  surface,  and  0 
the  eye  of  the  observer  at  an  elevation  h 
above  A.  The  line  drawn  perpendicular 
to  OC  is  truly  horizontal  (regarding  the 
earth  as  spherical),  while  the  tangent  OB 

is  the  line  drawn  from  0  to  B,  the  visible  horizon.     The  angle 
HOB  is  the  dip,  and  is  obviously  equal  to  OCB. 
From  the  triangle  OCB  we  have 


FIG.  31.  —  Dip  of  the 
Horizon 


cos  OCB  =  CB/  CO  = 
designating  the  dip  by  A. 


=  cos  A, 


66 


CORRECTIONS  TO  ASTRONOMICAL  OBSERVATIONS      67 

The  formula  in  this  shape  is  inconvenient,  because  it  deter-  Formui»for 
mines  a  small  angle  by  means  of  its  cosine.    But  since  1  —  cos  A 
=  2  sin2  £  A,  we  easily  obtain  the  following : 


h) 

Or,  since  A  is  always  a  small  angle,  and  neglecting  h  in  the 
denominator  of  the  fraction  as  being  insignificant  compared 
with  jft,  we  get 


This  gives  with  quite  sufficient  accuracy  the  true  depression 
of  the  sea  horizon  as  it  would  be  if  the  line  of  sight  were  straight. 
But  this  is  not  the  case,  owing  to  refraction  of  the  rays  in  pass- 
ing through  the  air,  and  the  amount  of  this  refraction  is  very 
uncertain  and  variable.  Ordinarily  the  dip  is  diminished  about 
one  eighth  of  the  amount  computed  by  the  formula. 

An  approximate  formula,  obtained  by  substituting  the  radius 
of  the  earth  (20  890000  feet)  and  reducing,  gives  A'  (i.e.,  in 


minutes  of  arc)  =  3438  (Sec.  9),  whence  A' 

mula  for 

=  V h  (feet)   (nearly) ;  or,  in  words,  the  dip  in  minutes  of  arc  dip. 

equals  the  square  root  of  the  observer's  elevation  in  feet;  i.e., 
the  dip  is  1'  at  an  elevation  of  1  foot,  5'  at  an  elevation  of 
25  feet,  10'  at  an  elevation  of  100  feet,  etc. 

This  result  is  generally  about  five  per  cent  too  large,  taking  into  account 
refraction ;  but  it  is  near  enough  for  most  practical  purposes,  since  at  sea 
the  observer  is  seldom  as  much  as  50  feet  above  the  sea-level  and  cannot, 
with  a  sextant,  measure  altitudes  more  closely  than  to  the  nearest  quarter 
of  a  minute. 

The  formula  A'  =  V3  h  (meters)  agrees  still  more  nearly  with  the  actual 
value. 


68 


MANUAL   OF   ASTRONOMY 


The  distance  OB  of  the  sea  horizon  is  easily  seen,  from  Fig.  31,  to  be 

3  h 


Formula  for 

distance  of      R  tan  A.      An    approximate   formula  is,   distance  in  miles  = 

sea  horizon. 


This,  however,  takes  no  account  of  refraction,  and  the  actual  distance  is 
always  greater. 


General 
definition  of 
parallax. 


Annual  or 

heliocentric 

parallax. 


Diurnal  or 
geocentric 
parallax. 


Horizontal 
parallax. 


78.  Parallax  (Fig.  32).  —  In  general  the  word  "parallax" 
means  the  difference  between  th^  direction  of  a  heavenly  body 
as  seen  by  the  observer  and  as  seen  from  some  standard  point 
of  reference. 

The  annual  or  heliocentric  parallax  of  a  star  is  the  difference 

of  the  star's  direction  as  seen 
from  the  earth  and  from  the  sun. 
With  this  we  have  nothing  to  do 
for  the  present. 

The  diurnal  or  geocentric  paral- 
lax of  the  sun,  moon,  or  a  planet 
is  the  difference  of  its  direction 
as  seen  from  the  center  of  the 
earth  and  from  the  observer's  sta- 
tion on  the  earth's  surface ;  or, 
what  comes  to  the  same  thing, 
it  is  the  angle  at  the  body  made 
by  two  lines  drawn  from  it,  one  to  the  observer,  the  other  to 
the  center  of  the  earth.  In  Fig.  32  the  parallax  of  the  body 
P  is  the  angle  OP C,  which  equals  xOP,  and  is  the  difference 
between  ZOP  and  ZCP.  Obviously  this  parallax  is  zero  for  a 
body  directly  overhead  at  Z,  and  a  maximum  for  a  body  rising 
at  H.  Moreover,  and  this  is  to  be  specially  noted,  this  paral- 
lax of  a  body  at  the  horizon  —  the  horizontal  parallax — is 
simply  t he  angular  semidiameter  of  the  earth  as  seen  from  the 
body.  When  we  say  that  the  moon's  horizontal  parallax  is  57', 
it  is  equivalent  to  saying  that,  seen  from  the  moon,  the  earth 
has  an  apparent  diameter  of  114'. 


FIG.  32.  — Parallax 


CORRECTIONS  TO  ASTRONOMICAL  OBSERVATIONS      69 

79.   Law  of  the  Parallax.  —  From  the  triangle  OOP  we  have 

PC  :  OC  =  sin  COP  :  sin  CPO, 
or,  R  :  r  =  sin  f  :  sin  p  (since  C  OP  is  the  supplement  of  ?). 

This  gives  Formula 

Sin^  =  -Sm?,  (a)  embodying 

jg  the  laws 

of  diurnal 

or,  since  p  is  always  a  small  angle,  parallax. 

p"  =  206265"  -  sin  £  (b) 

£kt 

When  a  body  is  at  the  horizon  its  zenith-distance  is  90°  and 
sin  f=l.  Hence,  the  horizontal  parallax,  II",  of  the  body  is 
given  by  the  formula 

sinn  =  -,     or     II"  =  206265-,     (<?);    and  /'  =  II"  sin  ?.     (d) 
./?  It 

Or,  in  words,  the  parallax  at  any  altitude  equals  the  horizontal 
parallax  multiplied  by  the  sine  of  the  apparent  zenith-distance. 

From  equation  (<?)  we  have  also,  for  finding  R,  the  distance  Relation 

Of   the  body,  between  dis- 

tance  of  a 


*=  or  £  =  ,  (e}  body  and  its 

Sin  II  II"  parallax. 

a  relation  of  great  importance  as  determining  the  distance  of  a 
heavenly  body  when  its  parallax  is  known. 

80.  Equatorial  Parallax.  —  Owing  to  the  "  ellipticity,"  or 
"  oblateness,"  of  the  earth,  the  horizontal  parallax  of  a  body 
varies  slightly  at  different  places,  being  a  maximum  at  the 
equator,  where  the  distance  of  an  observer  from  the  earth's 
center  is  greatest.  It  is  agreed  to  take  as  the  standard  the 
equatorial-horizontal-parallax,  i.e.,  the  earth's  equatorial  semi-  Equatorial 
diameter  in  seconds  as  seen  from  the  body.  parallax. 

If  the  earth  were  exactly  spherical,  the  parallax  would  act 
in  an  exactly  vertical  plane  and  would  simply  diminish  the 
altitude  of  the  body  without  in  the  least  affecting  its  azimuth. 


70 


MANUAL   OF   ASTRONOMY 


Really,  however,  it  acts  along  great  circles  drawn  from  the  geo- 
centric zenith  to  the  geocentric  nadir  (Sec.  11),  and  these  circles 
are  not  identical  with  the  vertical  circles  nor  exactly  normal  to 
the  horizon.  For  this  reason  the  azimuth  of  the  moon,  which 
has  a  parallax  of  about  a  degree,  is  sensibly  affected.  The 
calculation  of  the  parallax  corrections  to  observations  of  the 
moon's  right  ascension  and  declination  is  also  modified  and 
greatly  complicated.  (See  Campbell's  Practical  Astronomy, 
Sec.  26.) 

In  the  calculation  of  the  parallax  of  all  other  bodies  it  is 
sufficient  to  regard  the  earth  as  spherical. 

81.  Semidiameter.  —  In  the  case  of  the  sun  or  moon  the 
edge,  or  limb,  of  the  object  is  usually  observed,  and  to  get  the 
true  position  of  its  center  the  angular  semidiameter  must  be 
added  or  subtracted.  For  all  objects  except  the  moon  this  may 
be  taken  directly  from  the  ephemerides,  but  the  moon's  appar- 
ent diameter  increases  slightly  with  its  altitude,  being  about 
FIT  Par^  °r  about  30",  greater  when  in  the  zenith  than  at  the 
horizon,  because  at  the  zenith  it  is  about  4000  miles,  or  ^ 
part  of  its  whole  distance  from  the  center  of  the  earth,  nearer 
than  at  the  horizon.  At  any  observed  zenith-distance,  OP 
(Fig.  32),  the  apparent  or  "augmented"  semidiameter  («'),  as 
seen  from  0,  is  greater  than  the  semidiameter  (*)  given  in  the 
ephemeris  as  seen  from  C,  in  the  ratio  of  PC  to  PO.  From 
the  triangle  P  OC  we  obtain,  therefore, 

sf :  s::PC:PO:  :  sinPOC:  sinPCO:  :  sin  f :  sin  (£—  p) 
(f  being  the  apparent  zenith-distance). 


Whence 


sn 


sin(f— 


This  "augmentation"  of  the  moon's  diameter,  amounting  to  about 
30"  near  the  zenith,  has,  of  course,  nothing  whatever  to  do  with  the  opti- 
cal illusion  already  referred  to  which  makes  the  moon  seem  larger  when 
near  the  horizon. 


CORRECTIONS  TO  ASTRONOMICAL  OBSERVATIONS       71 


82.  Refraction.  —  As  the  rays  of  light  from  a  star  enter  our 
atmosphere,  unless  they  strike  perpendicularly  they  are  bent 
downwards  by  refraction  and  follow  a  curved  path,  as  illus- 
trated in  Fig.  33. 

Since  the  object  is  seen  in  the  direction  from  which  the  rays 
enter  the  eye,  the  effect  is  to  make  the  apparent  altitude  of  the 
object  greater  than  the  true. 

Refraction,  like  parallax,  is  zero  at  the  zenith  and  a  maxi- 
mum at  the  horizon,  where  under  average  conditions  it  lifts  an 
object  about  35',  leaving  the  azimuth,  however,  unchanged.  But 
the  law  of  refraction  is  very  different 
from  that  of  parallax. 

Its  amount  depends  upon  the  den- 
sity of  the  air  (which  is  determined 
by  the  barometric  pressure  and  tem- 
perature) as  well  as  the  altitude  of 
the  object,  but  is  independent  of  its 
distance. 

The    theory   of    refraction   is    too 


Astro- 
nomical 
refraction. 


Its  effect  to 
increase  the 
apparent 
altitude  of  a 
body. 


7?' 


FIG.  33.— Atmospheric  Refraction 


complicated  to  be  discussed  here,  and 

the  reader  is  referred  to  Campbell's  or  Chauvenet's  Practical 

Astronomy. 

The  computation  of  the  correction  when  precision  is  required 
is  made  by  means  of  elaborate  tables  provided  for  the  purpose  and 
given  in  works  on  practical  astronomy,  the  data  being  the  observed 
altitude  of  the  object,  the  temperature,  and  the  height  of  the 
barometer.  Increase  of  atmospheric  pressure  slightly  increases 
the  refraction,  and  increase  of  temperature  diminishes  it. 

For  altitudes  exceeding  25°  the  following  approximate  for- 
mula, corresponding  to  a  temperature  of  zero  Centigrade 
(32°  Fahrenheit)  and  a  barometric  pressure  of  30  inches,  may 
be  used,  and  will  generally  give  results  correct  within  a  few 
seconds,  viz.,  r"  =  60". 7  tan  ?,  in  which  £  is  the  apparent  zenith- 
distance. 


Affected  by 
temperature 
and  baro- 
metric 
pressure. 


Approxi- 
mate for- 
mulae for 
bodies  above 
15°  altitude. 


72 


MANUAL   OF   ASTRONOMY 


Refraction 
table  in 
Appendix. 


Effect  of 
refraction  to 
increase 
length  of 
the  day  at 
expense  of 
the  night. 


The  following  formula  (due  to  Professor  Comstock)  is  a  little 
more  complicated,  but  much  more  accurate,  viz., 


r»  = 


9835 
460 + 


tan 


in  which  b  is  the  height  of  the  barometer  in  inches  and  t  is  the 
temperature  on  Fahrenheit's  scale.  For  altitudes  above  15° 
this  formula  will  seldom  be  over  V  in  error. 

The  little  Table  VIII  (Appendix)  gives  by  inspection  pretty 
accurately  the  refraction  under  the  circumstances  stated  in  its 
heading ;  and  by  applying  the  approximate  corrections  for 
barometer  and  thermometer  indicated  in  the  note  below  it,  the 
results  will  seldom  be  more  than  2"  in  error. 

It  is  hardly  necessary  to  add  that  this  refraction  correction, 
required  by  most  astronomical  observations  of  position,  is  very 
troublesome,  and  usually  involves  more  or  less  uncertainty 
and  error  from  the  continually  changing  and  unknown  condi- 
tion of  the  atmosphere  along  the  path  followed  by  the  rays  of 
light. 

For  methods  by  which  the  amount  of  the  refraction  is  deter- 
mined by  observation,  the  reader  is  referred  to  works  on  practical 
astronomy,  or  to  the  author's  General  Astronomy,  Art.  94. 

83,  Effect  of  Refraction  near  the  Horizon.  —  The  horizontal 
refraction,  ranging  as  it  does  from  32'  to  40',  according  to 
meteorological  conditions,  is  always  somewhat  greater  than  the 
diameter  of  either  the  sun  or  the  moon.  At  the  moment, 
therefore,  when  the  sun's  lower  limb  appears  to  be  just  rising 
or  setting,  the  whole  disk  is  really  below  the"  plane  of  the  hori- 
zon ;  and  the  time  of  sunrise  in  our  latitudes  is  thus  accelerated 
from  two  to  four  minutes,  according  to  the  inclination  of  the 
sun's  diurnal  circle  to  the  horizon,  which  varies  with  the  time 
of  the  year.  Of  course,  sunset  is  delayed  by  the  same  amount, 
and  thus  at  both  ends  the  day  is  lengthened  at  the  expense  of 
the  night. 


CORRECTIONS  TO   ASTRONOMICAL  OBSERVATIONS       73 

Near  the  horizon  the  refraction  changes  very  rapidly ;  while  Effect  of 

under  ordinary  summer  temperature  it  is  about  35'  at  the  hori-  refraction 

zon,  it  is  only  29'  at  an  elevation  of  half  a  degree,  so  that  as  form  of  the 

the  sun  or  moon  rises  the  bottom  of  the  disk  is  lifted  6'  more  disks  of  sun 

than  the  top  and  the  vertical  diameter  is  thus  made  apparently  when  °°"y 

about  one-fifth  part  shorter  than  the  horizontal.     This  quite  near  the 
notably  distorts  the   disk  into  the  form  of  an  oval  flattened 
on  the  under  side.     In  cold  weather  the  effect  is  much  more 
marked. 

Two  other  semi-astronomical  effects,  the  twinkling  of  the 
stars  and  twilight,  are  due  to  the  action  of  our  atmosphere,  and 
may  be  treated  in  this  connection,  though  in  no  other  way  con- 
nected with  the  principal  subject  of  the  chapter. 

84.    Twinkling  or  Scintillation  of  the  Stars.  —  This  is  a  purely  Scintilla- 
atmospheric  phenomenon,  usually  conspicuous  near  the  horizon,  t 
where  it   is  often  accompanied  by  marked  changes  of    color,  phenome- 
Near  the  zenith  it  generally  disappears,  and  at  other  altitudes  non' 
it  differs  greatly  on  different  nights.     As  a  rule  only  the  stars 
twinkle  strongly ;  the  planets,  Mercury  excepted,  usually  shine 
with  an  almost  steady  light. 

Authorities  differ  as  to  the  details  of  explanation,  but  prob- 
ably scintillation  is  mainly  due  to  two  cooperating  causes,  both 
depending  on  the  fact  that  the  air  is  generally  full  of  streaks 
and  wavelets  of  unequal  density  carried  by  the  wind. 

(1)  Light  coming  through  such  a  medium  is  concentrated  in  Unequal 
some  places  and  diverted  from  others  by  simple  refraction,  like  refractlons 

by  drifting 

light  from  an  electric  lamp  shining  through  an  ordinary  window-  atmospheric 
pane  upon  the  opposite  wall.    If  the  light  of  a  star  were  strong  wavelets  of 
enough,  a  white  surface  illuminated  by  it  would  be  covered  by  density, 
bright  and  dark  mottlings,  drifting  with  the  wind ;  and  as  such 
mottlings  pass  the  eye  the  star  appears  to  fade  and  brighten  by 
turns.     Looked  at  in  the  telescope,  it  also  "dances,"  being 
slightly  displaced  back  and  forth  by  the  irregular  refraction. 


74 


MANUAL   OF   ASTRONOMY 


Supplemen- 
tary action 
of  optical 
"  inter- 
ference." 


Effect  upon 
the  spec- 
trum of  a 
star. 


Why  planets 
do  not 
twinkle. 


(2)  The  other  cause  of  twinkling  is  optical  interference.  Pen- 
cils of  light  coming  from  a  star  (optically  a  mere  luminous 
point]  reach  the  observer's  eye  by  routes  differing  only  slightly, 
and  are  just  in  a  condition  to  "interfere."  The  result  is 
the  temporary  destruction  of  rays  of  certain  wave-lengths  and 
the  reinforcement  of  others.  Accordingly,  the  "spectrum" 
(Sec.  569)  of  a  twinkling  star  is  traversed  by  dark  bands  in  the 
different  colors,  oscillating  back  and  forth,  but,  on  the  whole, 
when  the  star  is  rising,  progressing  from  the  blue  towards  the 
red,  and  vice  versa  when  the  star  is  near  the  setting. 

The  planets  do  not  twinkle,  because  they  are  not  luminous 
points,  but  have  disks  made  up  of  a  congeries  of  such  points ; 
while  each  point  twinkles  like  a  star,  the  twinklings  do  not 
synchronize  with  each  other,  and  so  the  general  sum  of  light 
remains  practically  uniform.  When  very  near  the  horizon,  how- 
ever, the  irregular  refraction  is  sometimes  sufficiently  violent 
to  make  them  dance  and  change  color.  Since  the  disk  of 
Mercury  is  very  small,  and  the  planet  is  never  seen  except 
near  the  horizon,  it  usually  behaves  like  a  star. 

85.  Twilight.  —  This  is  caused  by  the  reflection  of  sunlight 
from  the  upper  portion  of  the  earth's  atmosphere,  perhaps  from 
the  air  itself,  perhaps  from  the  minute  solid  particles  in  the  air, 
—  authorities  differ.  After  the  sun  has  set,  its  rays,  passing 
over  the  observer's  head,  still  continue  to  shine  through  the  air 
above  him,  and  twilight  continues  as  long  as  any  portion  of  the 
illuminated  air  remains  in  sight  from  where  he  stands.  It  is  con- 
sidered to  end  when  stars  of  the  sixth  magnitude  become  visible 
near  the  zenith,  which  does  not  occur  until  the  sun  is  about 
18°  below  the  horizon;  but  this  varies  considerably  for  different 
places,  according  to  the  purity  of  the  air. 

Duration  of          The  length  of  time  required  by  the  sun  after  setting  to  reach  this  depth 

twilight.         varies  with  the  season  and  with  the  observer's  latitude.     In  latitude  40°  it 

is  about  ninety  minutes  on  March  1  and  October  12,  but  more  than  two 

hours  at  the  summer  solstice.     In  latitudes  above  50°,  when  the  days  are 


Cause  of 
twilight. 


CORRECTIONS  TO  ASTRONOMICAL  OBSERVATIONS      75 

longest,  twilight  never  disappears  even  at  midnight.  On  the  mountains 
of  Peru,  on  the  other  hand,  it  is  said  never  to  last  more  than  half  an  hour, 
probably  because  the  upper  air  in  that  region  is  practically  clear  from  dust 
particles. 

From  the  fact  that  twilight  lasts  until  the  sun  is  1 8°  below  the  horizon,    Height  of 
the  height  of  the  twilight-producing  atmosphere  can  easily  be  computed,    the  earth's 
and  comes  out  about  50  miles.      This,  however,  is  not  the  real  limit  of  a 
the  atmosphere.      The  phenomena  of  meteors  show  that  at  an  elevation 
of  100  miles  there  is  still  air  enough  to  resist  their  motion  and  cause  their 
incandescence. 

Soon  after  the  sun  has  set,  the  twilight  bow  appears  rising  in  the  east,  —   The  twilight 
a  dark  blue  segment,  bounded  by  a  faintly  reddish  arc.     It  is  the  shadow   b°w. 
of  the  earth  upon  the  air,  and  as  it  rises  the  arc  becomes  rapidly  diffuse 
and  indistinct  and  is  lost  long  before  it  reaches  the  zenith. 


EXERCISES 

V  1.  What  is  the  approximate  dip  of  the  horizon  from  a  hill  900  feet 
high  (Sec.  77)?  Jo'/*«c 

(/  2.  How  high  must  a  mountain  be  in  order  that  the  dip  of  the  horizon 
from  its  summit  may  be  2°?  /fy  y  r* 

3.  What  is  the  distance  of  the  horizon  in  miles,  as  seen  from  the 
summit  of  this  mountain  (Sec.  77)  ? 

\/  4.  Assuming  the  horizontal  parallax  of  the  sun  at  8".  8,  what  is  the 
horizontal  parallax  of  Mars  when  nearest  us,  at  a  distance  of  0.378  astro- 
nomical units?  (The  astronomical  unit  is  the  distance  from  the  earth  to 
the  sun.) 

5.  What  is  the  greatest  apparent  diameter  of  the  earth  as  seen  from 
Mars? 

v     6.  What  is  the  horizontal  parallax  of  Jupiter  when  at  a  distance  of  6 
astronomical  units? 

/  7.  Does  atmospheric  refraction  increase  or  decrease  the  apparent  size 
of  the  sun's  disk  when  it  is  near  the  horizon? 

8.  What  is  the  lowest  latitude  where  twilight  can  last  all  night?     Can 
it  do  so  at  New  York?  at  London?  at  Edinburgh? 


CHAPTER    IV 


Funda- 
mental 
problems  of 
observation. 


Definitions 
of  astronom- 
ical latitude. 


FUNDAMENTAL   PROBLEMS   OF  PRACTICAL  ASTRONOMY 

Latitude  —  Time  —  Longitude  —  Azimuth — The  Eight  Ascension  and  Declination  of 

a  Heavenly  Body 

86.  There  are  certain  problems  of  practical  astronomy  which 
are   encountered   at   the   very  threshold  of   all  investigations 
respecting  the  heavenly  bodies,  the  earth  included.     The  student 
must  know  how  to  determine  his  position  on  the  surface  of  the 
earth,  that  is,  his  latitude  and  longitude  ;  how  to  ascertain  the 
exact  time  at  which  an  observation  is  made;  and  how  to  observe 
the  precise  position  of  a  heavenly  body  and  fix  its  right  ascen- 
sion and  declination. 

87.  Definitions  of  the  Observer's  Latitude.  —  In  geography 
the  latitude  of  a  place  is  usually  defined  simply  as  its  distance 
north  or  south  of  the  equator,  measured  in  degrees.     This  is 
not  explicit  enough  unless  it  is  stated  how  the  degrees  them- 
selves are  to  be  measured.     If  the  earth  were  a  perfect  sphere 
there  would  be  no  difficulty,  but  since  the  earth  is  sensibly 
flattened  at  its  poles  the  geographical  degrees  have  somewhat 
different  lengths  in  different  parts  of  the  earth.     The  funda- 
mental  definition   of   astronomical  latitude    has  already  been 
given  (Sec.   32)   as  the  angle  between  the  direction  of  gravity 
where  the  observer  stands  and  the  plane  of  the  equator.      The 
angle  between  gravity  and  the  earth's  axis  is  the  colatitude  of 
the  place.     Other  equivalent  definitions  of  the  latitude  are  the 
altitude  of  the  pole  and  the  declination  of  the  zenith,  which  is 
the  same  as  the  altitude  of  the  pole,  as  is  clear  from  Fig.  34, 
where  ZQ  obviously  equals  NP. 

76 


PROBLEMS  OF  PRACTICAL  ASTRONOMY 


77 


The  problem,  then,  is  to  determine  by  observation  of  the  heav- 
enly bodies  either  the  angle  of  elevation  of  the  celestial  pole,  or  the 
distance  in  degrees  between  the  zenith  and  the  celestial  equator. 

88.  First  Method:   by  Observation  of  Circumpolar  Stars. - 
The  most  obvious  method  (already  referred  to)  is  by  observing 
with  a  suitable  instrument  the  altitude  of  some  star  near  the 
pole  at  the  moment  .when  it  is  crossing  the  meridian  above 
the  pole,  and  again  twelve  sidereal  hours  later  when  it  is  once 
more  on  the  meridian  but  below  the  pole.     In  the  first  case  its 
altitude  is  the  greatest  possible;  in  the  second,  the  least.     The 
mean  of  the  two  altitudes  (each  corrected  for  atmospheric  refrac- 
tion) is  the  altitude  of  the  pole  or  the  latitude  of  the  observer. 

The  method  has  the  great  advantage  that  it  is  an  independent 
one;  that  is,  the  observer  is  not  obliged  to  depend  upon  his 
predecessors  for  any  of  his  data.     But  the  method  fails  for 
stations    very    near    the 
equator,    because    there 
the    pole  is  so  near  the 
horizon   that   the   neces- 
sary observations  cannot 
be  made. 

At  an  observatory  the 
observations  are  usually 
made  with  the  meridian- 
circle,  and  the  mean  of  a 

great  number  of  observations  is  necessary  in  order  to  elimi- 
nate the  slight  errors  in  the  computed  refraction  corrections 
due  to  varying  atmospheric  conditions.  Where  the  meridian- 
circle  is  not  available,  the  observations  may  also  be  made 
with  a  sextant  or  theodolite,  but  the  results  are  much  less 
precise. 

89.  Second  Method:   by   the    Meridian    Altitude    or   Zenith- 
Distance  of  a  Body  whose  Declination  is  accurately  known.— 
In  Fig.  34  the  circle  MQPN  is  the  meridian,  Q  and  P  being 


Latitude  by 
observation 
of  circum- 
polar  stars- 


Advantages 
and  disad- 
vantages of 
the  method. 


FIG.  34 


T8 


MANUAL   OF   ASTRONOMY 


Latitude  by 
meridian 
altitude  of 
object  of 
known 
declination. 


Formula  for 
latitude  in 
this  case. 


Advantages 
and  disad- 
vantages of 
this  method. 


Latitude  at 
sea  by 
observation 
of  the  sun. 


respectively  the  equator  and  the  pole  and  Z  the  zenith.  QZ  is 
the  declination  of  the  zenith,  or  the  latitude  of  the  observer.  If, 
when  the  star  s  crosses  the  meridian,  we  observe  its  zenith- 
distance,  fa  (Zs  in  the  figure),  its  declination,  Qs  or  Sg  being 
known,  then  evidently  QZ  equals  Qs  plus  %Z\  that  is,  the  latitude 
equals  the  declination  of  the  star  plus  its  zenith-distance.  If  the 
star  were  at  s',  south  of  the  equator,  the  same  equation  would 
still  hold  algebraically,  because  the  declination  Qs'  is  then  a 
negative  quantity ;  and  if  the  star  were  at  n  between  the  zenith 
and  pole,  its  north  zenith-distance,  fw,  would  be  negative.  In 
all  cases,  therefore,  we  may  write  <j>  =  8  +  £. 

If  we  use  the  meridian-circle  in  making  our  observations,  we  can 
always  select  stars  that  pass  near  the  zenith,  where  the  refraction  is  small, 
which  is  in  itself  a  great  advantage.  Moreover,  we  can  select  them  in 
such  a  way  that  some  will  be  as  much  north  of  the  zenith  as  others  are 
south,  and  this  will  practically  eliminate  even  the  slight  refraction  errors  that 
remain.  On  the  other  hand,  in  using  this  method  we  have  to  obtain  our 
star  declinations  from  the  catalogues  made  by  previous  observers,  so  that 
the  method  is  not  an  "  independent "  one. 

90.  At  sea  the  latitude  is  usually  obtained  by  observing  with 
the  sextant  the  sun's  maximum  altitude,  which  occurs,  of  course, 
at  noon.  Since  at  sea  one  seldom  knows  beforehand  precisely 
the  moment  of  local  noon,  the  observer  takes  care  to  begin  his 
observations  some  minutes  earlier,  repeating  his  measure  of  the 
sun's  altitude  every  minute  or  two.  At  first  the  altitude  will 
keep  increasing,  but  immediately  after  noon  occurs  it  will  begin  to 
decrease.  The  observer  uses,  therefore,  the  maximum1  altitude 
obtained,  which,  corrected  for  refraction,  parallax,  semidiameter, 
and  dip  of  the  horizon,  will  give  him  the  true  meridian  altitude 
of  the  sun.  The  Nautical  Almanac  gives  him  its  declination. 

10n  account  of  the  sun's  motion  in  declination  and  the  northward  or 
southward  motion  of  the  ship  itself,  the  sun's  maximum  altitude  is  usually 
attained  not  precisely  on  the  meridian,  but  a  short  time  earlier  or  later.  This 
requires  a  slight  correction  to  the  deduced  latitude,  the  calculation  of  which 
is  explained  in  books  on  navigation. 


PROBLEMS  OF  PRACTICAL  ASTRONOMY       79 

91.  Third   Method:    by  Circummeridian   Altitudes.  —  If  the  Latitude  by 
observer  knows  his  time  with  reasonable  accuracy,  he  can  obtain  c 

his  latitude  from  observations  of  the  altitude  of  a  heavenly  body  altitudes. 
made  when  it  is  near  the  meridian  with  practically  the  same 
precision  as  at  the  moment  of  meridian  passage.    It  lies  beyond 
our  scope  to  discuss  the  method  of  reduction,  which  is  explained, 
with  the  necessary  tables,  in  all  works  on  practical  astronomy. 

The  great  advantage  of  the  method  is  that  the  observer  is 
not  restricted  to  a  single  observation  at  each  meridian  passage 
of  the  sun  or  of  the  selected  star,  but  can  utilize  the  half-hours 
preceding  and  following  that  moment.  The  meridian-circle,  of 
course,  cannot  be  used.  Usually  the  sextant,  or  a  so-called 
"universal  instrument"  (Sec.  70),  is  employed. 

92,  Fourth  Method1 :  by  the  Zenith-Telescope.  —  The  essential  Latitude  by 

characteristic  of  the  method  is  the  measurement  with  a  microm-  the  zemth~ 

telescope  — 
eter  of  the  d  iffe  r  ence  between  the  nearly  equal  zenith-distances  the  most 

of  two   stars  which  pass   the   meridian  within   a  few   minutes  accurate 
of  each  other,  one  north  and  the  other  south  of  the  zenith,  and 
not  very  far  from  it;  such  pairs  of  stars  can  now  always  be 
found  in  our  star-catalogues. 

A  special  instrument,  known  as  the  zenith-telescope,  is  gen- 
erally employed,  though  a  simple  transit-instrument,  provided 
with  reversing  apparatus,  a  delicate  level  attached  to  the  tele* 
scope,  and  a  declination  micrometer  is  now  often  used. 

Fig.  35  shows  the  very  complete  zenith-telescope  of  the  Flower  Observa- 
tory near  Philadelphia. 

At  the  Georgetown  Observatory  a  photographic  zenith-telescope  is  used, 
having  a  photographic  plate  in  place  of  the  eyepiece. 

The  telescope  is  set  at  the  proper  altitude  for  the  star  which  Method  of 
first  comes  to  the  meridian  and  the  "  latitude  level,"  as  it  is  c 
called,  —  which  is  attached  to  the  telescope  —  is  set  horizontal ; 

1  Known  as  the  "American  method,"  because  first  practically  introduced 
by  Captain  Talcott,  of  the  United  States  Engineers,  in  a  boundary  survey  in 
1845.  It  is  now  very  generally  adopted  and  considered  the  best. 


80 


MANUAL   OF   ASTRONOMY 


Advantage 
in  dispens- 
ing with  a 
graduated 
circle. 


as  the  star  passes  through  the  field  of  view  its  distance  north 
or  south  of  the  central  horizontal  wire  is  measured  by  the 
micrometer.  The  instrument  is  then  reversed  so  that  the  tele- 
scope points  towards 
the  north  (if  it  was 
south  before),  and 
the  telescope  so 
readjusted,  if  neces- 
sary, that  the  level 
is  again  horizontal, 
—  taking  great  care, 
however,  not  to 
disturb  the  angle 
between  the  level  and 
the  telescope  itself. 
The  telescope  is  then 
evidently  elevated 
at  exactly  the  same 
angle  as  before,  but 
on  the  opposite  side 
of  the  zenith.  As 
the  second  star 
passes  through  the 
field,  we  measure 
with  the  micrometer 
its  distance  north  or 
south  of  the  central 
wire.  The  compari- 
son of  the  two  measures  gives  the  difference  of  the  two  zenith- 
distances  with  great  accuracy  and  without  the  necessity  of 
depending  upon  any  graduated  circle. 

In  field  operations  like  those  of  geodesy  this  is  an  enormous 
advantage,  both  as  regards  the  portability  of  the  instrument 
and  the  attainable  precision  of  results. 


FIG.  35.  — A  Zenith-Telescope 
By  Warner  &  Swasey 


PROBLEMS   OF   PRACTICAL   ASTRONOMY  81 

From  Fig.  34  we  have 

for  star  south  of  zenith,  </>  =  Sg  -+-  £  ; 
for  star  north  of  zenith,  <£  =  8n  —  fn. 


Adding  the  two  equations  and  dividing  by  2,  we  have 

—  (TA 
2      / 


—  (T  Formula  for 

the  latitude. 


The  star-catalogue  gives  us  the  declinations  of  the  two  stars 
(&,+&n)  ;  and  the  difference  of  the  zenith-distances  (fg  —  fj  is 
determined  by  the  micrometer  measures. 

When  the  method  was  first  introduced  it  was  difficult  to  find 
pairs  of  stars  whose  declination  was  known  with  sufficient  pre- 
cision. At  present  our  star-catalogues  are  so  extensive  and 
exact  that  this  difficulty  has  practically  disappeared. 

Refraction  is  almost  eliminated,  because  the  two  stars  of  each  Refraction 
pair  are  at  very  nearly  the  same  zenith-distance.  eliminated. 

Evidently  the  accuracy  depends  ultimately  upon  the  exactness  with 
which  the  level  measures  the  slight  but  inevitable  difference  between  the 
inclinations  of  the  instrument  when  pointed  on  the  two  stars. 

In  Dr.  Chandler's  Almucantar  (Sec.  67)  the  telescope  preserves  its 
constant  declination  automatically,  by  being  mounted  upon  a  base  which 
floats  in  mercury,  thus  dispensing  with  the  level. 

There  are  numerous  other  methods  for  obtaining  the  latitude.  In 
Chauvenet's  Practical  Astronomy  over  forty  are  given,  some  of  which  can 
fairly  compete  in  precision  with  those  named  above. 

93,    The  Gnomon.  —  The  ancients  could  not  use  any  of  the  Ancient 
preceding  methods  for  finding  the  latitude.     They  were,  how-  method  of 

J  determining 

ever,  able  to  make  a  very  respectable  approximation  by  means  the  latitude 
of  the   simplest  of  all  astronomical  instruments,  the  gnomon.  bythe 
This  is  merely  a  vertical  shaft  or  column  of  known  height 
erected  on  a  perfectly  horizontal  plane,  and  the  observation 


82 


MANUAL   OF   ASTRONOMY 


Climate." 


consists  in  noting  the  length  of  the  shadow  cast  at  noon 
at  certain  times  of  the  year.  Suppose,  for  instance,  that  on 
the  day  of  the  summer  solstice,  at  noon,  the  length  of  the 
shadow  is  AC  (Fig.  36).  The  height  AB  being  given,  we  can 
easily  compute  in  the  right-angled  triangle  the  angle  ABC, 
which  equals  SBZ,  the  sun's  zenith-distance  when  farthest 
north. 

Again,  observe  the  length  AD  of  the  shadow  at  noon  of  the 
shortest  day  in  winter  and  compute  the  angle  ABD,  which  is  the 
sun's  corresponding  zenith-distance  when  farthest  south.  Now, 
since  the  sun  travels  equal  distances  north  and  south  of  the 

celestial  equator,  the  mean 
of  the  two  zenith-distances 
will  give  the  angular  dis- 
tance between  the  equator 
and  the  zenith,  i.e.,  the 
declination  of  the  zenith, 
which  is  the  latitude  of 
the  place. 

The  method  is  an  inde- 
pendent one,  like  that  of 
the  observation  of  circum- 
polar  stars,  requiring  no 
data  except  those  which 
the  observer  determines  for  himself.  It  does  not  admit  of  much 
accuracy,  however,  since  the  penumbra  at  the  end  of  the  shadow 
makes  it  impossible  to  measure  its  length  very  precisely. 

It  should  be  noted  that  the  ancients,  instead  of  designating  the  position 
of  a  place  by  means  of  its  latitude,  used  its  climate;  the  climate  (from 
/cAtjua)  being  the  slope  of  the  plane  of  the  celestial  equator,  the  angle 
AEB,  which  is  the  colatitude. 

For  the  use  of  the  gnomon  in  determining  the  obliquity  of  the  ecliptic 
and  the  length  of  the  year,  see  Sees.  164  (2)  and  182.  Many  of  the  Egyp- 
tian obelisks  are  known  to  have  been  used  for  astronomical  observations, 
and  perhaps  were  erected  mainly  for  that  purpose. 


FIG.  36.  —  Latitude  by  the  Gnomon 


PROBLEMS  OF  PRACTICAL  ASTRONOMY 


83 


94.   Variation  of  Latitude  and  Motion  of  the  Poles  of  the  Earth. 

—  It  has  long  been  doubted  whether  latitudes  are  strictly  con- 
stant. They  cannot  be  so  if  the  axis  of  the  earth  shifts  its 
position  within  the  globe.  Some  have  supposed  that  in  the 
past  there  have  been  great  changes  of  this  kind,  seeking  thus 
to  explain  certain  geological  epochs,  as,  for  instance,  the  glacial 
and  the  carboniferous.  But  thus  far  no  evidence  of  any  consid- 
erable displacement  has  appeared,  nor  is  there  any  satisfactory 
proof  of  certain  slow, 
continuous  "  secular  " 
changes,  which  have 
been  strongly  sus-  -< 
pected. 

Theoretically,  how-   -°"10' 
ever,  any  alteration  in 
the  arrangement  of  the 
matter   of   the   earth, 

-  +0*10 


+  0?20 


•0?20.- 


+  OJ30 


FIG.  37 


by  elevation,  subsi- 
dence,  transportation, 
or  denudation,  must  +°':2°t- 
necessarily  disturb  the 
axis  and  change  the 
latitudes  to  some  ex- 
tent. The  question 

is  merely  whether  our  observations  can  be  made  sufficiently 
accurate  to  detect  the  change.  Since  1889  the  limit  has  been 
reached,  and  we  now  have  conclusive  proof  of  such  effects. 

The  first  satisfactory  evidence  of  the  fact  was  obtained  at 
Berlin  by  Kiistner,  and  at  other  German  stations  in  1888  and 
1889,  and  the  result  has  since  been  abundantly  confirmed  by 
observations  at  many  other  stations.  Moreover,  Dr.  S.  C. 
Chandler  of  Cambridge,  U.S.,  by  a  brilliant  and  laborious  series 
of  investigations,  finds  the  same  variations  clearly  exhibited  in 
almost  every  extended  body  of  reliable  observations  made  since 


No  evidence 
of  any 
considerable 
changes  in 
the  position 
of  the 
earth's  axis. 


Minute 
changes 
theoretically 
must  occur. 


First  obser- 
vational 
evidence 
obtained 
in  1888. 


84 


MANUAL   OF   ASTRONOMY 


Nature  of 
the  periodic 

motion  of 

the  pole. 


1750.  From  the  whole  mass  of  evidence  he  concludes  that 
the  movement  of  the  pole  at  present  is  composed  of  two 
motions,  —  one  an  annual  revolution  in  an  ellipse  about  30 
£QQ^  iong  but  varying  in  width  and  position,  the  other  a  revo- 

J  ... 

lution  in  a  circle  about  26  feet  in  diameter  and  having  a  period 
of  about  4-28  days,  —  both  revolutions  being  counter-clockwise. 
The  resultant  motion  presents  a  very  irregular  appearance  and 
changes  greatly  from  year  to  year. 

Fig.  37  represents  the  actual  motion  from  1890  to  1898  as  deduced  by 
Albrecht  from  all  available  observations. 

The  annual  component  of  this  polar  motion  is  very  likely  due  to  meteoro- 
logical causes  which  follow  the  seasons,  such  as  the  deposit  of  rain,  snow, 
and  ice.  The  explanation  of  the  428-day  component  is  not  yet  entirely 
clear,  and  its  discussion  would  take  us  too  far. 

It  is  likely  also  that  irregular  disturbances,  due  to  various  causes  —  for 
instance,  perhaps,  earthquakes  —  may  modify  the  regular  periodic  motions. 


Time  de- 
fined as 
measured 
duration. 


Determina- 
tion of  time. 


The  three 
kinds  of 
time. 


95.  Different  Kinds  of  Time.  —  Time  is  usually  defined  as 
measured  duration.  From  the  beginning  the  apparent  diurnal 
rotation  of  the  heavens  has  been  accepted  as  the  standard  unit, 
and  to  it  we  refer  all  artificial  measures  of  time,  such  as  clocks 
and  watches. 

In  practice  the  accurate  determination  of  time  consists  in 
finding  the  Hour  Angle  (Sec.  21)  of  the  object  or  point  which 
has  been  selected  to  mark  the  beginning  of  the  day  by  its  passage 
across  the  meridian. 

In  astronomy  three  kinds  of  time  are  now  recognized:  side- 
real time,  apparent  solar  time,  and  mean  solar  time,  —  the  last 
being  the  tijne  of  civil  life  and  ordinary  business,  while  the 
first  is  used  for  astronomical  purposes  exclusively.  Apparent 
solar  time  (formerly  called  true  time)  has  now  practically  fallen 
out  of  use,  except  in  countries  where  watches  and  clocks  are 
scarce  or  unknown  and  sun-dials  are  the  ordinary  timekeepers. 


PROBLEMS  OF  PRACTICAL  ASTRONOMY       85 

96.  Sidereal  Time.  —  The   celestial  object  which  determines  Sidereal 
sidereal  time  by  its  position  in  the  sky  at  any  moment  is,  it  time~ the 

J          t  hour  angle 

will  be  remembered,  the  vernal  equinox  or  first  of  Aries  (symbol,   Of  the  vernal 
°f ),  i.e.,  the  point  where  the  sun  crosses  the  celestial  equator  e(iuinox' 
in  the  spring,  about  March  21  every  year. 

As  already  stated  (Sec.  25),  the  local  sidereal  day1  begins  at 
the  moment  when  the  first  of  Aries  crosses  the  observer's 
meridian,  and  the  sidereal  time  at  any  moment  is  the  hour 
angle  of  the  vernal  equinox;  i.e.,  it  is  the  time  marked  by  a 
clock  so  set  and  adjusted  as  to  show  sidereal  noon  (OhOmOs)  at 
each  transit  of  the  first  of  Aries. 

The  equinoctial  point  is,  of  course,  invisible ;  but  its  posi- 
tion among  the  stars  is  always  known,  so  that  its  hour  angle  at 
any  moment  can  be  determined  by  observing  the  stars. 

97,  Apparent  Solar  Time.  —  Just  as  sidereal  time  is  the  hour  Apparent 
angle   of  the   vernal   equinox,   so  apparent   solar  time   at   any  s<jlartime- 
moment  is  the  hour  angle  of  the  sun.     It  is  the  time  shown  by  angle  of  the 
the  sun-dial,  and  its  noon  occurs  at  the  moment  when  the  sun's  sun:  identi- 

cal  with  sun 

center  crosses  the  meridian.  dial  time. 

On  account  of  the  earth's  orbital  motion  (explained  more 
fully  in  Chapter  VI),  the  sun  appears  to  move  eastward  along 
the  ecliptic,  completing  its  circuit  in  a  year.  Each  noon, 
therefore,  it  occupies  a  place  among  the  stars  about  a  degree 
farther  east  than  it  did  the  noon  before,  and  so  comes  to  the 
meridian  about  four  minutes  later,  if  time  is  reckoned  by  a 
sidereal  clock.  In  other  words,  the  solar  day  is  about  four 
minutes  longer  than  the  sidereal,  the  difference  amounting  to 
exactly  one  day  each  year,  which  contains  366  J  sidereal  days. 

But  the  sun's  eastward  motion  is  not  uniform,  for  several 

1  On  account  of  the  precession  of  the  equinoxes  (to  be  discussed  later),  the 
sidereal  day  thus  denned  is  slightly  shorter  than  it  would  be  if  denned  as  the 
interval  between  successive  transits  of  some  given  star  ;  the  difference  being  a 
little  less  than  Tfo.  of  a  second,  or  one  day  in  25800  years,— too  little  to  be 
worth  taking  into  account  in  any  ordinary  calculation. 


86 


MANUAL   OF   ASTRONOMY 


Apparent 
solar  days 
vary  in 
length. 
Hence  ap- 
parent time 
is  unsatisfac- 
tory. 


reasons,  and  the  apparent  solar  days  therefore  vary  in  length. 
December  23,  for  instance,  is  about  fifty-one  seconds  longer 
from  sun-dial  noon  to  noon  again  (by  a  sidereal  clock)  than  Sep- 
tember 16.  For  this  reason  apparent  solar  or  sun-dial  time  is 
unsatisfactory  for  scientific  use  and  cannot  be  kept  by  any  simple 
mechanical  arrangement  in  clocks  and  watches.  At  present  it 
is  practically  discarded  in  favor  of  mean  solar  time. 

98,  Mean  Solar  Time A  fictitious  sun  is,  therefore,  imagined, 

moving  uniformly  eastward  in  the  celestial  equator  and  complet- 
ing its  annual  course  in  exactly  the  same  time  as  that  in  which 
the  actual  sun  makes  the  circuit  of  the  ecliptic.     This  fictitious 
sun  is  made  the  timekeeper  for  mean  solar  time.     It  is  mean 
noon  when  its  center  crosses  the  meridian,  and  at  any  moment 
the  hour  angle  of  the  fictitious  sun  is  the  mean  time  for  that 
moment.     The  mean  solar  days  are,  therefore,  all  of  exactly 
the  same  length  and  equal  to  the  length  of  the  average  apparent 
solar  day,  the  mean  solar  day  being  longer  than  the  sidereal  by 
3m55s.91  (mean  solar  minutes  and  seconds)  and  the  sidereal  day 
shorter  than  the  solar  by  3m568.55  (sidereal  minutes  and  seconds). 

99.  Sidereal   time   will    not   answer  for    business    purposes, 
because   its   noon    (the   transit  of  the   vernal   equinox)   occurs 
at  all  hours  of  the  day  and  night  in  different  seasons  of  the 
year :    on  September  22,  for  instance,  it   comes   at  midnight. 
Apparent  solar  time  is  unsatisfactory  because  of  the  variation 
in  the   length  of  its   days   and  hours.     Yet  we  have  to  live 
by  the  sun:   its  rising  and  setting,  daylight  and  night,  control 
our  actions. 

Mean  solar  time  furnishes  a  satisfactory  compromise.  It  has 
a  time  unit  which  is  invariable,  and  it  can  be  kept  by  clocks  and 
watches,  while  it  agrees  nearly  enough  with  sun-dial  time  for 
convenience.  It  is  the  time  now  used  for  all  purposes  except 
in  some  kinds  of  astronomical  work. 

The  difference  between  apparent  time  and  mean  time  (never 
amounting  to  more  than  about  a  quarter  of  an  hour)  is  called 


PROBLEMS  OF  PRACTICAL  ASTRONOMY       87 

the  equation  of  time  and  will  be  discussed  hereafter  in  connec-  Equation  of 

tion  with  the  earth's  orbital  motion  (Sec.  174).  time- 

Since  there  are  365.2421  solar  days  in  a  year  (Sec.  182)  and  Relation 

one  more  sidereal  day,  we  have  the  following  fundamental  rela-  between  the 

^  ...  number  of 

tion:  —  the  number  of  sidereal  seconds  in  any  time  interval  :  the  sidereal  and 

number  of  mean  solar  seconds  in  the  same  interval  :  :  366.2421  :  mean  solar 

secondsina 


given  time 

From  this  it  follows  at  once  that  to  reduce   a  solar  time  interval. 
interval  to  sidereal,  we  must  divide  the  number  of  seconds  it  Reduction  of 
contains  by  365.2421,  and  add  the  quotient  to  the  number  of  asolartime 

17  interval  to 

solar  seconds.     To  reduce  a  sidereal  interval  to  solar,  divide  by  sidereal,  and 
366.2421,  and  subtract  the  quotient  from  the  number  of  sidereal  vice  versa- 
seconds. 

The  Nautical  Almanac  gives  the  sidereal  time  of  mean  solar 
noon  for  every  day  of  the  year,  with  tables  by  means  of  which 
mean  solar  time  can  be  accurately  deduced  from  the  correspond- 
ing sidereal  time,  or  vice  versa,  by  a  very  brief1  calculation. 

100,   The  Civil  Day  and  the  Astronomical  Day.  —  The  astro-  Theastro- 
nomical  day  begins  at  mean  noon;  the  civil  day,  twelve  hours  nomical  and 

civil  cljiv^ 

earlier  at  midnight.  Astronomical  mean  time  is  reckoned 
around  through  the  whole  twenty-four  hours  instead  of  being 
counted  in  two  series  of  twelve  hours  each:  thus,  10  A.M.  of 
Wednesday,  February  27,  civil  reckoning,  is  Tuesday,  February 
26,  22  o'clock,  by  astronomical  reckoning.  This  must  be  borne 
in  mind  in  using  the  Almanac.2 

1  The  approximate  relation  between  sidereal  time  and  mean  solar  time  is  very 
simple.      Assuming  that  on  March  22  the  two  times  agree,  after  that  day  the 
sidereal  time  gains  two  hours  each  month.     On  April  22,  therefore,  the  sidereal 
clock  is  two  hours  in  advance,  on  June  22,  six  hours  in  advance,  and  so  on. 
On  account  of  the  differing  length  of  months,  this  reckoning  is  slightly  errone- 
ous in  some  parts  of  the  year,  but  is  usually  correct  within  four  or  five  minutes. 
March  22  is  taken  as  the  starting-point  because  it  distributes  the  errors  better 
than  the  21st.     For  the  odd  days  the  gain  may  be  taken  as  four  minutes  daily. 

2  The  astronomical  day  is  made  to  begin  at  noon  because  astronomers  are 
"night-birds,"  and  would  find  it  inconvenient  to  have  to  change  dates  at 
midnight  in  the  middle  of  their  work. 


88 


MANUAL    OF   ASTRONOMY 


Determina- 
tion of  time 
consists  in 
ascertaining 
the  error 
of  a  time- 
piece. 


Determina- 
tion of  time 
by  the 
transit- 
instrument. 


Almanac 

stars. 


Necessary 
to  observe  a 
number  of 
stars  in 
order  to 
attain  high 
precision. 


DETERMINATION   OF   TIME 

In  practice  the  problem  of  determining  time  always  consists 
in  ascertaining  the  error  or  correction  of  a  timepiece,  i.e.,  the 
amount  by  which  the  clock  or  chronometer  is  faster  or  slower 
than  the  time  it  ought  to  indicate. 

101.  Determination  of  Time  by  the  Transit-Instrument.  — The 
method  most  employed  by  astronomers  is  by  observations  with 
the  transit-instrument  (Sec.  61).  We  observe  the  time  shown  by 
the  sidereal  clock  at  which  a  star  of  known  right  ascension  crosses 
each  wire  of  the  reticle.  The  mean  is  taken  as  the  instant  of 
crossing  the  instrumental  meridian,  and  when  the  instrument 
is  in  perfect  adjustment  the  difference  between  the  star's  right 
ascension  and  the  observed  clock  time  will  be  the  clock's 
"error";  or,  as  a  formula,  A£  =  a  —  £, —  At  being  the  usual 
symbol  for  the  clock  error,  and  t  the  observed  time. 

The  Almanac  supplies  a  list  of  several  hundred  stars  whose 
right  ascension  and  declination  are  accurately  given  for  every 
tenth  day  of  the  year,  so  that  the  observer  at  night  has  no  diffi- 
culty in  finding  a  suitable  star  at  almost  any  time.  In  the  day- 
time he  is,  of  course,  limited  to  the  brighter  stars. 

The  observation  of  a  single  star  with  an  instrument  in  ordi- 
nary adjustment  will  usually  give  the  error  of  the  clock  within 
half  a  second;  but  it  is  much  better  and  usual  to  observe  a 
number  of  stars,  reversing  the  instrument  upon  its  Y's  once  at 
least  during  the  operation.  This  will  enable  him  to  determine 
and  allow  for  the  faults  of  instrumental  adjustment,  so  that 
with  a  good  instrument  a  skilled  observer  can  thus  determine 
his  clock  error  within  about  a  thirtieth  of  a  second  of  time, 
provided  proper  correction  is  applied  for  his  "  personal  equa- 
tion" (Sec.  64). 

If  instead  of  observing  a  star  we  observe  the  sun  with  this 
instrument,  the  time  as  shown  by  the  mean  solar  clock  ought  to 
be  twelve  hours  plus  or  minus  the  equation  of  time  as  given  in 


PROBLEMS  OF  PRACTICAL  ASTRONOMY       89 

the  Almanac.     But  for  various  reasons  transit  observations  of  Soiartime 
the  sun  are  less  accurate  than  those  of  the  stars,  and  it  is  far  usually  now 

deduced 

better  to  deduce  the  mean  solar  time  from  the  sidereal  time  by  from 
means  of  the  almanac  data.  sidereal. 

102.  The  Method  of  Equal  Altitudes. — If  we  observe  the  time 
shown  by  the  chronometer  or  the  clock  when  a  star  attains  a  Method  of 
certain  altitude  and  then  the  time  when  it  attains  the  same  equal 

altitudes. 

altitude  on  the  other  side  of  the  meridian,  the  mean  of  the  two 
times  will  be  the  time  of  the  star's  transit  across  the  meridian, 
provided,  of  course,  that  the  chronometer  runs  uniformly  during 
the  interval. 

We  may  also  use  stars  of  slightly  differing  declination,  one  Modification 
on  one   side   of   the  meridian,   and   the  other  observed  a  few  ofthe 

method  in 

minutes  later  on  the  other  side;  and  by  a  somewhat  tedious  observing 
calculation  it  is  possible  to  determine  the  error  of  the  clock  starsof 
with  practically  the  same  accuracy  as  if  both  observations  had  different 
been  made  on  the  same  star,  and  much  more  quickly.  declination. 

If  we  observe  the  sun  in  this  manner  in  the  morning,  and 
again  in  the  afternoon,  the  moment  of  apparent  noon  will  seldom  Correction 
be  exactly  half-way  between  the  two  observed  times,  and  proper  re(iulred  m 
correction  must  be  made  for  the  sun's  slight  motion  in  decli-  time  from 
nation  during1  the  interval,  —  a  correction  easilv  computed  bv  e<iual  alti~ 

,    ,  ,         ,         .  °    ,    ,        ^,  J    tudesofthe 

tables  furnished  for  the  purpose.  sun 

The  advantage  of  this  method  is  that  the  errors  of  gradua- 
tion of  the  instrument  have  no  effect,  nor  is  it  necessary  for  the 
observer  to  know  his  latitude  except  approximately. 

On  the  other  hand,  there  is,  of  course,  danger  that  the  second 
observation  may  be  interfered  with  by  clouds.  Moreover,  both 
observations  must  be  made  at  the  same  place. 

103.  Marine  Method:  by  a  Single  Altitude  of  the  Sun,  the  Observation 
Observer's  Latitude  being  known.  — Since  neither  of  the  preced-  todetermine 

time  at  sea- 

ing  methods  can  be  used  at  sea,  the  following  is  the  method 
usually  practised.  The  altitude  of  the  sun,  at  some  time  when 
it  is  rapidly  rising  or  falling  (i.e.,  not  near  noon),  is  measured 


90 


MANUAL   OF   ASTRONOMY 


Computa- 
tion of  the 
time  from 
the  obser- 
vation. 


Time  when 
observation 
should  be 
made. 


with   the  sextant,  and  the   corresponding  time  shown  by  the 

chronometer  accurately  noted. 

We  then  compute  the  hour  angle  of  the  sun,  P,  from  the 

triangle  PZS  (Fig.  38),  and  this  hour  angle,  corrected  for  the 

equation  of  time,  gives  the  mean  solar  time  at  the  observed 

moment.     The   difference   between  this  time  and  that  shown 

by  the  chronometer  is  the  error  of  the  chronometer  on  local 

time. 

In  the  triangle  ZPS  (which  is  the  same  as  SPO  in  Fig.  8)  all 

three  of  the   sides  are   given :  PZ  is   the  complement  of  the 

latitude  c/>,  which  is  sup- 
posed to  be  known ;  PS 
is  the  complement  of  the 
sun's  declination  8,  which 
is  found  in  the  Almanac,  as 
is  also  the  equation  of  time; 
while  ZS  or  f  is  given 
by  observation,  being  the 
complement  of  the  sun's 
altitude  as  measured  by  the 

sextant   and  corrected  for  dip,  semidiameter,   refraction,  and 

parallax.     The  formula  ordinarily  used  is 


EH 

FIG.  38.  —  Determination  of  Time  by  the 
Sun's  Altitude. 


8in  ! 


=  J  s 
* 


~  8)]  sin  j  [g  -  0  - 


cos 


cos  8 


In  order  to  insure  accuracy  it  is  desirable  that  the  sun 
should  be  on  the  prime  vertical,  or  as  near  it  as  practicable. 
It  should  NOT  be  near  the  meridian,  for  at  that  time  the  sun 
is  rising  or  falling  very  slowly,  and  the  slightest  error  in  the 
measured  altitude  would  make  an  enormous  difference  in  the 
computed  hour  angle.  If  the  sun  is  exactly  east  or  west  at 
the  time  of  observation,  an  error  of  even  several  minutes  of 
arc  in  the  assumed  latitude  produces  no  sensible  effect  upon 
the  result. 


PROBLEMS  OF  PRACTICAL  ASTRONOMY       91 

The  disadvantage  of  the  method  is  that  any  error  of  gradua-  Disadvan- 
tion  of  the  sextant  vitiates  the  result,  and  no  sextant  is  perfect.  tage  of  the 

method  and 

But  with  ordinary  care  and  good  instruments  the  sea-captain  is  limit  of 
able  to  get  his  time  correct  within  three  or  four  seconds.  accuracy. 

When  a  number  of  altitude  observations  have  been  made  for  time,  and 
it  is  desired  to  reduce  them  separately,  so  as  to  test  their  agreement  and 
determine  their  probable  error,  there  is  an  advantage  in  using  the  formula 

cos  £  ,> 

cos  P  = - — _  —  tan  d>  tan  d, 

cos  $  cos  8 

employing  the  "  Gaussian  logarithms  "  in  the  computation.  The  second 
term  of  the  formula  and  the  denominator  of  the  first  term  remain  constant 
through  the  whole  series,  saving  much  labor  in  reduction. 

104.   To  compute  the  Time  of  Sunrise  or  Sunset.  —  To  solve  Calculation 
this  problem  we  have  precisely  the  same  data  as  in  finding  the  of  time  of 
time  by  a  single  altitude  of  the  sun.     The  zenith-distance  of  the  sunset. 
sun's  center  at  the  moment  when  its  upper  edge  is  rising  equals 
90°  51',  —  made  up  of  90°  plus  16'  (the  mean  semidiameter  of 
the  sun)  plus  35'  (the  mean  refraction  at  the  horizon).      The 
resulting  hour  angle,  corrected  for  the  equation  of  time,  gives 
the  mean  local  time  at  which  the  sun's  upper  limb  reaches  the 
horizon  under  average  circumstances  of  temperature  and  baro- 
metric pressure.     If  the  sun  rises  or  sets  over  the  sea  horizon 
and  the  observer's  eye  is  at  any  considerable  elevation  above 
sea-level,  the  dip  of  the  horizon  must  also  be  added  to  90°  51; 
before  making  the  computation. 

The  beginning  and  end  of  twilight  may  be  computed  in  the 
same  way  by  merely  substituting  108°,  i.e.,  90°  +  18°,  for 
90°  51'. 

DETEEMINATION   OF   LONGITUDE 

Having  now  the  means  of  finding  the  true  local  time  at  any 
place,  we  can  take  up  the  problem  of  the  longitude,  the  most 
important  of  all  the  economic  problems  of  astronomy.  The  great 
observatories.  a.t  Greenwich  and  Paris  were  established  expressly 


92 


MANUAL   OF   ASTRONOMY 


Definition  of 
longitude. 


Difference 
of  longitude 
equals  dif- 
ference of 
local  times. 


The  knot 
of  the 
problem. 


Telegraphic 
method. 


Details  of 
process. 


for  the  purpose  of  furnishing  the  observations  which  could  be 
utilized  for  its  accurate  determination  at  sea. 

105,  The  longitude  of  a  place  on  the  earth  may  be  defined  as  the 
angle  at  the  pole  of  the  earth  between  the  standard  meridian  and  the 
meridian  of  the  place;  and  this  angle  is  measured  by,  and  equal 
to,  the  arc  of  the  equator  intercepted  between  the  two  meridians. 

As  to  the  standard  meridian  there  is  some  variation  of  usage. 
At  sea  nearly  all  nations  at  present  reckon  from  the  meridian  of 
Greenwich,  except  the  French,  who  insist  on  Paris. 

Since  the  earth  turns  011  its  axis  at  a  uniform  rate,  the  angle 
at  the  pole  is  strictly  proportional  to  the  time  required  for  the 
earth  to  turn  through  that  angle ;  so  that  longitude  may  be,  and 
now  usually  is,  expressed  in  time  units,  —  i.e.,  in  hours,  minutes, 
and  seconds,  rather  than  degrees,  etc.,  —  and  is  simply  the  differ- 
ence between  the  local  times  at  G-reenwich  and  at  the  place  where 
the  longitude  is  to  be  determined. 

Since  the  observer  can  determine  his  own  local  time  by  the 
methods  already  given,  the  knot  of  the  problem  is  to  find  the 
Greenwich  local  time  corresponding  to  his  own,  without  leaving 
his  place. 

106.  First  Method:  by  Telegraphic  Comparison  between  his 
Own  Clock  and  that  of  Some  Station  whose  Longitude  from  Green- 
wich is  known.  —  The  difference  between  the  two  clocks  will 
be  the  difference  of  longitude  between  the  two  stations  after 
the  proper  corrections  for  clock  errors,  personal  equation,  and 
time  occupied  by  the   transmission  of  the   electric  signals   have 
been  applied  or  eliminated. 

The  process  usually  employed  is  as  follows  :  The  observers,  after  ascer- 
taining that  they  both  have  clear  weather,  proceed  early  in  the  evening 
to  determine  the  local  time  at  each  station  by  an  extensive  series  of  star 
observations  with  the  transit-instrument.  Then  at  an  hour  agreed  upon 
the  observer  at  the  eastern  station,  A,  "  switches  his  clock  "  into  the  tele- 
graphic circuit,  so  that  its  beats  are  communicated  along  the  line  and 
received  upon  the  chronograph  of  the  western  station.  After  the  eastern 
clock  has  thus  sent  its  signals,  say  for  two  minutes,  it  is  "  switched  out " 


PKOBLEMS  OF  PRACTICAL  ASTRONOMY       93 

and  the  western  observer  puts  his  clock  into  the  circuit,  so  that  its  beats 
are  received  upon  the  eastern  chronograph.  Sometimes  the  signals  are 
communicated  both  ways  simultaneously,  so  that  the  beats  of  both  clocks 
appear  upon  both  chronograph  sheets  at  the  same  time.  The  operation  is 
closed  by  another  series  of  transit  observations  by  each  observer. 

We  have  now  upon  each  chronometer  sheet  an  accurate  comparison  of  the 
two  clocks,  showing  the  amount  by  which  the  western  clock  is  slow  of  the 
eastern,  and  if  the  transmission  of  electric  signals  were  instantaneous, 
the  difference  shown  upon  the  two  chronometer  sheets  would  be  identical 
on  both.     Practically,  however,  there  will  always  be  a  discrepancy  of  some   Elimination 
hundredths  of  a  second,  amounting  to  twice  the  time  occupied  in  the  trans-   of  error  due 
mission  of  the  signals;  but  the  mean  of  the  two  differences  after  correcting   to  tr^ns~ 
for  the  carefully  determined  clock  errors  will  be  the  true  difference  of  longi-   time  and 
tude  between  the  places.     Especial  care  must  be  taken  to  determine  with   personal 
accuracy  the  personal  equations  of  the  observers,  or  else  to  eliminate  them,  which    equation, 
may  be  done  by  causing  the  observers  to  change  places. 

In  cases  where  the  highest  accuracy  is  required,  it  is  customary  to  make 
observations  of  this  kind  on  not  less  than  five  or  six  evenings. 

The  astronomical  difference  of  longitude  between  two  places  Limit  of 

can  thus  be  determined  within  about  ^  of  a  second  of  time,  i.e.,  8 
within  about  20  feet  in  the  latitude  of  the  United  States. 

107.    Second  Method :  by  the  Chronometer.  —  This  method  is  The  chrono- 

available  at  sea.     The  chronometer  is  set  to  indicate  Greenwich  metric 

,          ,  .      ,  .  55  i        •         i  method  of 

time  before  the  ship  leaves  port,  its  "  rate     having  been  care-  determining 
fully  determined  by  observation  for  several  days.     In  order  to  longitude 
find  the  longitude  by  the  chronometer,  the  sailor  must  determine 
its  "  error  "  upon  local  time  by  an  observation  of  the  altitude  of 
the  sun  when  near  the  prime  vertical  (Sec.  103).     If  the  chro- 
nometer indicates  true  Greenwich  time,  its  "error"   deduced 
from  the  observation  will  be  the  longitude.     Usually,  however, 
the  indication  of  the  chronometer  face  must  be  corrected  for 
the  gain  or  loss  of  the  chronometer  since  leaving  port,  in  order 
to  give  the  true  Greenwich  time  at  the  moment. 

Chronometers  are    only   imperfect    instruments,    and    it    is  Chr0nome- 
important,  therefore,  that  several  of  them  should  be  carried  by  ters  needed 
the  vessel  to  check  each  other.     This  requires  three  at  least,  g^  other 


94 


MANUAL   OF   ASTRONOMY 


Failure  of 
the  method 
for  long 
voyages. 


Lunar 
method,  the 
moon  being 
regarded  as 
a  clock  hand 
showing 
Greenwich 
time. 


Lunar 
methods 
available 
on  land. 


Lunar 
distances 
at  sea. 


because  if  only  two  chronometers  are  carried,  and  they  disagree, 
there  is  nothing  to  indicate  which  is  the  delinquent. 

Moreover,  in  the  course  of  months,  chronometers  generally 
change  their  rates  progressively,  so  that  they  cannot  be  depended 
on  for  very  long  intervals  of  time ;  and  the  error  accumulates 
much  more  rapidly  than  in  proportion  to  the  time.  If,  there- 
fore, a  ship  is  to  be  at  sea  more  than  three  or  four  months 
without  making  port,  the  method  becomes  untrustworthy. 
For  voyages  of  less  than  a  month  it  is  now  practically  all 
that  could  be  desired. 

108.  Third  Method :  by  the  Moon  regarded  as  a  Clock  Hand, 
with  Stars  for  Dial  Figures.  —  Before  the  days  of  reliable  chro- 
nometers, navigators  and  astronomers  were  generally  obliged  to 
depend  upon  the  moon  for  their  Greenwich  time.  The  laws 
of  her  motion  are  now  fairly  well  known,  so  that  the  right 
ascension  and  declination  of  the  moon  are  now  computed  and 
published  in  the  Nautical  Almanac,  three  years  in  advance,  for 
every  Greenwich  hour  of  every  day  in  the  year.  It  is  therefore 
possible  to  deduce  the  Greenwich  time  at  any  moment  when 
the  moon  is  visible  by  making  some  observation  which  will 
accurately  determine  her  place  among  the  stars. 

On  land  it  may  be : 

(a)  The  direct  transit-instrument  observation  of  her  right 
ascension  as  she  crosses  the  meridian. 

(6)  The  observation  at  the  moment  when  she  occults  a  star 
(incomparably  the  most  accurate  of  all  lunar  methods)  or  makes 
contact  with  the  sun  in  a  solar  eclipse. 

(c)  The  observation  of  the  moon's  azimuth  with  the  universal 
instrument  at  an  accurately  determined  time. 

At  sea  the  only  practicable  observation  is  to  measure  with 
a  sextant  a  lunar  distance,  i.e.,  the  distance  of  the  moon  from 
some  star  or  planet  nearly  in  her  path. 

Since,  however,  the  almanac  place  of  the  moon  is  the  place  she  would 
apparently  occupy  if  seen  from  the  center  of  the  earth,  most  lunar 


PROBLEMS   OF  PRACTICAL   ASTRONOMY  95 

observations  require  complicated  and  laborious  reductions  before  they  can  Inferiority 

be  used  for  longitude.     Moreover,  the  motion  of  the  moon  is  so  slow  (she  of  the  lunar 

requires  a  month  to  make  the  circuit  of  360°)  that  any  error  in  the  methods> 

observation  of  her  place  produces  nearly  thirty  times  as  great  an  error  in  ° 
the  corresponding  Greenwich  time  and  the  deduced  longitude.     It  is  as  if 
one  should  try  to  read  accurate  time  from  a  watch  that  had  only  an  hour- 
hand. 

109.  Other  Methods:  Eclipses  of  the  Moon  and  Jupiter's  Satellites.  —  Longitude 
A  rough  longitude  can  be  obtained  from  the  observation  of  these  eclipses,  by  eclipses 
since  they  occur  at  the  same  moment  of  absolute  time  wherever  observed.  of  the  moon 
By  comparing  the  local   times   of  observation  with  the    Greenwich  time  T     .,    , 

eJU.pl  LOT  S 

obtained  by  correspondence  after  the  event,  or  from  the  Almanac,  the   satellites, 
difference  of  longitude  at  once  comes  out.     The  difficulty  with  this  method 
is  that  the  eclipses  are  gradual  phenomena,  presenting  no  well-marked 
instant  for  observation. 

On  the  same  principle  artificial  signals,  such  as  flashes  of  powder  and   Longitude 
explosion  of  rockets,  can  be  used  between  two  stations  so  situated  that   by  artificial 
both  can  see  the  flashes.     Early  in  the  century  the  difference  of  longitude    S1^na    • 
between  the  Black  Sea  and  the  Atlantic  was  determined  by  means  of  a 
chain  of  such  signal  stations  on  the  mountain  tops ;  so  also,  later,  the  differ- 
ence of  longitude  between  the  eastern   and  western  extremities  of  the 
northern  boundary  of  Mexico.     This  method  is  now  superseded  by  the 
telegraph. 

110.  Local  and  Standard  Time.  —  Until  recently  it  has  been  Local  and 
always  customary  to  use  local  time,  each  city  determining  its  J^da" 
own  time  by  its   own  observations.     Before  the   days   of  the 
telegraph,  and  while  traveling  was  comparatively  slow  and  infre- 
quent, this  was  best.     At  present  it  has  been  found  better  for 

many  reasons  to  give  up  the  system  of  local  times  in  favor  of  a 
system  of  standard  time.     This  facilitates  all  railway  and  tele-  Advantages 
graphic  business  in  a  remarkable  degree,  and  makes  it  practi-  °.f  standard 
cally  easy  for  every  one  to  keep  accurate  time,  since  it  can  be 
daily  wired  from  some  observatory  (as  Washington)  to  every 
telegraph  office  in  the  country.     According  to  the  system  now  American 
established  in  North  America,  there  are  five  such  standard  times  systems  of 

standard 

in  use,  —  the  colonial,  the  eastern,  the  central,   the  mountain,  time, 
and  the  Pacific,  —  which  are  slower  than  Greenwich  time  by 


96 


MANUAL   OF   ASTRONOMY 


exactly  four,   five,   six,   seven,   and   eight  hours,   respectively. 
The  minutes  and  seconds  are  everywhere  identical. 

At  most  places  only  one  of  these  standard  times  is  employed ; 
but  in  cities  where  different  systems  join  each  other,  as,  for 
instance,  at  Atlanta  and  Pittsburg,  two  standard  times  are  in 
use,  differing  from  each  other  by  exactly  one  hour,  and  from 
the  local  time  by  about  half  an  hour.  In  some  such  places  the 
local  time  also  maintains  itself. 

This  system  is  now  adopted  in  nearly  all  civilized  countries,  though  with 
a  half-hour  modification  in  certain  cases.  Everywhere  except  in  America 
the  standard  time  is  fast  of  Greenwich  time.  In  Continental  Europe, 
Russia  excepted,  it  is  one  hour  fast ;  in  Cape  Colony,  one  and  one-half 
hours ;  in  India,  five  and  one-half  hours  ;  in  Burma,  six  and  one-half  hours  ; 
in  West  Australia,  eight  hours ;  in  South  Australia  and  Japan,  nine  hours  ; 
in  Eastern  Australia,  ten  hours ;  and  in  New  Zealand,  eleven  and  one-half 
hours. 

In  order  to  determine  the  standard  time  by  observation  it 
is  only  necessary  to  determine  the  local  time  by  one  of  the 
methods  given,  correcting  it  by  first  adding  the  observer's  longi- 
tude west  from  Greenwich,  and  then  deducting  the  necessary 
integral  number  of  hours. 

111.  Where  the  Day  begins.  —  It  is  evident  that  if  a  traveler 
were  to  start  from  Greenwich  on  Monday  noon  and  were  by 
some  means  able  to  travel  westward  along  the  parallel  of  lati- 
tude as  fast  as  the  earth  turns  eastward  beneath  his  feet,  he 
would  keep  the  sun  exactly  upon  the  meridian  all  day  long 
and  have  continual  noon.  But  what  noon?  It  was  Monday 
noon  when  he  started,  and  when  he  gets  back  to  London 
twenty-four  hours  later  he  will  find  it  to  be  Tuesday  noon  there. 
Yet  it  has  been  noon  all  the  time.  When  did  Monday  noon 
become  Tuesday  noon  ? 

It  is  agreed  among  mariners  to  make  the  change  of  date  at  the 
180th  meridian  from  G-reenwich,  which  passes  over  the  Pacific 
hardly  anywhere  touching  the  land. 


PROBLEMS   OF   PRACTICAL   ASTRONOMY  97 

Ships  crossing   this   line  from   the   east  skip  one  day  in   so  Loss  or  gain 
doing1.     If  it   is   Monday  afternoon   when   a  ship  reaches   the  of  a  day  by 

vessels  pass- 
line,  it  becomes  Tuesday  afternoon  the  moment  she  passes  it,  ing  the 

the    intervening    twenty-four  hours   being   dropped   from   the  date-line. 
reckoning  on  the  log-book.      Vice  versa,  when  a  vessel  crosses 
the  line  from  the  western  side,  it  counts  the  same  day  twice 
over,  passing  from  Tuesday  back  to  Monday,  and  having  to  do 
Tuesday  over  again. 

There  is  considerable  irregularity  in  the  date  actually  used  on  the  The  date- 
different  islands  in  the  Pacific,  as  will  be  seen  by  looking  at  the  so-called   ^ne* 
date-line  as  given  in  the  Century  Atlas  of  the  World.     Those  islands  which 
received  their  earliest  European  inhabitants  via  the  Cape  of  Good  Hope  have 
adopted  the  Asiatic  date,  even  if  they  really  lie  east  of  the  180th  meridian ; 
while  those  that  were  first  approached  via  the  American  side  have  the 
American  date.     When  Alaska  was  transferred  from  Russia  to  the  United 
States,  it  was  necessary  to  drop  one  day  of  the  week  from  the  official  dates. 


PLACE   OF  A   SHIP   AT   SEA 

112.  Determination  of  the  Position  of  a  Ship.  —  The  determi- 
nation of  the  place  of  a  ship  at  sea  is  commercially  of  such 
importance  that,  notwithstanding  a  little  repetition,  we  collect 
here  the  different  methods  available  for  the  purpose.  They 
are  necessarily  such  that  the  requisite  observations  can  be 
made  with  the  sextant  and  chronometer,  the  only  instruments 
available  on  shipboard. 

The  latitude  is  usually  obtained  by  observations  of  the  sun's  Determine 
altitude  at  noon,  according  to  the  method  explained  in  Sec.  90.  tionof  a 

The  longitude  is  usually  found  by  determining  the  error  upon  tude  and 
local  time  of  the  chronometer,  which  carries  Greenwich  time.  longitude. 
(See  Sees.  103  and  10T.) 

In  case  of  long  voyages,  or  when  the  chronometer  has  for 
any  reason  failed,  the  longitude  may  also  be  obtained  by  meas- 
uring lunar  distances  and  comparing  them  with  the  data  of  the 
Nautical  Almanac. 


98 


MANUAL   OF   ASTRONOMY 


Sumner's 
method. 


The  circle 
of  position. 
Its  center 
and  radius 
at  any  time. 


Position  of 
ship  deter- 
mined by 
the  inter- 
section of 
two  circles 
of  position. 


Practical 
application 
of  the 
method. 


These  methods  require  separate  observations  for  the  latitude 
and  for  the  longitude. 

113.  Sumner's  Method.  —  At   present  a  method  known   as 
Sumners  Method,  because  first  proposed  by  Captain  Sumner  of 
Boston,  in  1843,  has  come  largely  into  use.     It  is  based  on  the 
principle  that  any  single  observation  of  the  sun's  altitude,  giving, 
of  course,  its  zenith-distance  at  the  time,  determines  the  so-called 
circle  of  position  on  which  the  ship  is  situated.     The  center  of 
this  circle  of  position  on  the  earth's  surface  is  the  point  directly 
under  the  sun  at  the  moment  of  observation.     The  longitude  of 
this  point  is  the    Greenwich  apparent  time  at  the  moment  of 
observation  as  determined  by  the  chronometer,  and  its  latitude 
is  the  sun's  declination.     The  radius  of  the  circle  of  position 
(reckoned  in  degrees  of  a  great  circle  from  this  center)  is  the 
observed  zenith-distance  of  the  sun. 

A  second  observation  made  some  hours  later  will  give  a 
second  circle  of  position,  and  if  the  ship  has  not  moved  mean- 
while the  intersection  of  the  two  circles  will  give  the  place  of 
the  ship. 

The  circles  intersect  at  two  points,  of  course,  but  at  which 
one  the  ship  is  situated  is  never  doubtful,  because  the  approxi- 
mate azimuth  of  the  sun,  observed  simply  as  a  compass  bearing, 
tells  roughly  on  what  part  of  the  circle  the  ship  is  placed. 
If,  for  instance,  the  sun  is  in  the  southeast  at  the  first  observa- 
tion, the  ship  must  be  on  the  northwestern  part  of  the  corre- 
sponding circle  of  position. 

If  the  ship  has  moved  between  the  two  observations,  as  of 
course  is  usual,  its  motion  as  determined  by  log  and  compass 
can  be  allowed  for  with  very  little  difficulty. 

114.  Usually  the  matter  is  treated  as-  follows  :   The  latitude  of  the 
vessel  is  practically  always  known  within  a  degree  or  so,  from  the  "  dead 
reckoning  "  since  the  last  observation.     Suppose  the  latitude  is  known  to 
be  about  51° ;   then,   from  the  first  (morning)  observation  of  the  sun's 
altitude  and  the  chronometer  'time,  the  navigator  computes  the  longitude, 


PROBLEMS  OF  PRACTICAL  ASTRONOMY 


99 


Longitude  West  from  Greenwich 


assuming  the  latitude  to  be  52°,  and  finds  it  to  be,  say,  40°  52'.  Again, 
assuming  the  latitude  to  be  50°,  he  gets  43°  20',  and  marks  the  two  com- 
puted longitudes  at  A  and  JB  on  the  chart  (Fig.  39).  A  line  drawn  through 
these  points  will  be  very  nearly  a  part  of  the  vessel's  circle  of  position  at 
the  time  of  that  observation. 

From   the   second   (afternoon)   observation   the  points   C  and  D  are 
computed  in  the  same  way,  giving  a  piece  of  the  second  circle  of  position. 

Suppose  now  that  in  the  interval  the  ship  has  moved  60  miles  on  a 
course  north  60°  west.  From  the  points  A  and  B  lay  off  60  miles  on  the 
chart  in  the  proper 
direction  to  the  points 
a  and  6,  and  join  ab 
by  a  line.  5',  the  in-  Lat. 
tersection  of  this  line 
with  the  line  CD,  will 
be  the  position  of  the 
ship  at  the  time  of 
the  second  observation 
with  all  the  approxi- 
mation necessary  for 
the  navigator's  pur- 
pose ;  and  if  we  reckon 
back  60  miles  from  £', 
we  shall  find  S,  the 
ship's  position  in  the 
morning.  There  are, 

however,  extended  tables  which  greatly  reduce  the  labor  of  computations 
and  make  the  result  more  accurate  than  that  derived  from  the  chart. 

The  peculiar  advantage  of  the  method  is  that  each  observa- 
tion is  used  for  all  it  is  worth,  giving  accurately  the  position  its  peculiar 
of  a  line  upon  which  the  vessel  is  somewhere  situated,  and  advantase- 
approximately  (by  the  sun's  azimuth)  its  position  on  that  line. 
Very  often  this  knowledge  is  all  that  the  navigator  needs  to 
give  him  the  knowledge  of  his  distance  from  land,  even  when 
he  fails  in  getting  the  second  observation  necessary  to  deter- 
mine his  precise  location.     Everything,  however,  depends  upon  Must  have 
the  correctness  of  the   Grreenwich  time  given  by  the  chronometer,   Greenwich 
just  as  in  the  ordinary  method  of  longitude  determination. 


4 

5°              4 

4°             4 

3°             4 

2°           4 

1°             4 

0° 

,at. 

5o° 

C 

^/^ 

/    "^ 

/ 

/ 

^ 

/ 

toO 

\ 

/ 

' 

/ 

4 

52 

\ 

\/ 

/ 

11° 

/\~- 

^     o  / 

/ 

M 

/ 

\ 

\7* 

/ 

/\ 

50° 

'"b    ~ 

!\*zl 

\D 

eno 

»" 

(XT         2* 

56m         2* 

52m           2' 

48™        2" 

44"         2* 

40" 

FIG.  39.  —  Sumner's  Method 


100 


MANUAL   OF   ASTRONOMY 


Determina- 
tion of 


of  pole-star. 


115,   Determination  of  "Azimuth."  —  A  problem,  important,   though 
not  so  often  encountered  as  that  of  latitude  and  longitude  determinations, 
.is  that  of  determining  the  "  azimuth,"  or  "  true  bearing,"  of  a  line  upon 
the  earth's  surface. 

With  a  theodolite  having  an  accurately  graduated  horizontal  circle  the 
observer  points  alternately  upon  the  pole-star  and  upon  a  distant  signal 
erected  for  the  purpose  at  a  distance  of  say  half  a  mile  or  more,  —  usually 
an  "  artificial  star "  consisting  of  a  small  hole  in  a  plate  of  metal,  with 
a  lantern  behind  it.  At  each  pointing  he  notes  the  time  by  a  sidereal 
chronometer.  The  theodolite  must  be  carefully  adjusted  for  collimation, 

and  especial  pains  must  be  taken  to  have  the 
axis  of  the  telescope  perfectly  level. 

The  next  morning  by  daylight  the  observer 
measures  the  angle  or  angles  between  the 
night  signal  and  the  objects  whose  azimuth 
is  required. 

If  the  pole-star  were  exactly  at  the  pole, 
the  mere  difference  between  the  two  readings 
of  the  circle,  obtained  when  the  telescope  is 
pointed  on  the  star  and  on  the  signal,  would 
directly  give  the  azimuth  of  the  signal.  As 
this  is  not  the  case,  the  azimuth  of  the  star 
must  be  computed  for  the  moment  of  each 
observation,  which  is  easily  done,  as  the 
right  ascension  and  declination  of  the  star 
are  given  in  the  Almanac  for  every  day  of  the  year. 

Referring  to  Fig.  40,  N  being  the  north  point  of  the  horizon,  P  the  pole, 
and  NZ  the  meridian,  we  see  that  PS  is  the  polar  distance  of  the  star,  or 
complement  of  its  declination,  the  side  PZ  is  the  complement  of  the 
observer's  latitude,  while  the  angle  at  P  is  the  hour  angle  of  the  star,  i.e., 
the  difference  between  the  right  ascension  of  the  star  and  the  sidereal  time 
of  observation.  This  hour  angle  must,  of  course,  be  reduced  to  degrees 
before  making  the  computation.  We  thus  have  two  sides  of  the  triangle, 
viz.,  PS  and  PZ,  with  the  included  angle  at  P,  from  which  to  compute 
the  angle  Z  at  the  zenith.  This  is  the  star's  azimuth. 

The  pole-star  is  used  rather  than  any  other  because,  being  so  near 
the  pole,  any  slight  error  in  the  assumed  latitude  of  the  place  or  in  the 
time  of  the  observation  will  produce  hardly  any  effect  upon  the  result, 
especially  if  the  star  be  observed  near  its  greatest  elongation  east  or  west 
of  the  pole. 


N    H  H' 

FIG.  40.  —  Determination  of 
Azimuth 


PROBLEMS  OF  PRACTICAL  ASTRONOMY      101 

The  sun,  or  any  other  heavenly  body  whose  position  is  given  in  the   Azimuth  by 
Almanac,  can  also  be  used  as  a  reference  point  in  the  same  way  when  near   tue  sun- 
the  horizon,  provided  sufficient  care  is  taken  to  secure  an  accurate  observa- 
tion of  the  time  at  the  instant  when  the  pointing  is  made.     But  the  results 
are  usually  rough  compared  with  those  obtained  from  the  pole-star. 

DETERMINATION   OF   THE   POSITION   OF   A 
HEAVENLY   BODY 

116.  The  "  position "  of  a  heavenly  body  is  defined  by  its 
right  ascension  and  declination.  These  may  be  determined : 

(1)  By  the  meridian-circle,  provided  the  body  is  bright  enough  Direct  deter 
to   be    seen   by  the    instrument   and   crosses  the  meridian  at  mmatlonof 

•>  i          •  i  both  c°ordi- 

night.     If  the  instrument  is  in  exact  adjustment,  the  sidereal  nates  of  a 
time   when  the   object  crosses  the   middle  wire   of  the   reticle  of  Body's  P°si 

.7  .  /.  .  tion  by  the 

the    instrument   is    directly    the    right    ascension    of    the    object.  meridian- 
Corrections  are  necessary  only  on  account  of  errors  of  the  clock,  circle 
errors  of  adjustment  of  the  instrument,  and  personal  equation 
of  the  observer.     Parallax  and  refraction  do  not  enter  into  the 
result.  * 

The  reading  of  the  circle  of  the  instrument,  corrected  for 
refraction,  and  for  parallax  if  necessary,  gives  the  polar  distance 
of  the  object  if  the  polar  point  of  the  circle  has  been  deter- 
mined, or  it  gives  the  zenith-distance  of  the  object  if  the 
nadir  point  has  been  determined  (Sec.  69).  In  either  case  the 
declination  can  be  immediately  deduced.  A  single  complete 
observation,  therefore,  with  the  meridian-circle,  determines  both 
the  right  ascension  and  declination  of  the  object.  In  order  to 
secure  accuracy,  however,  it  is  desirable  that  the  observations 
should  be  repeated  many  times. 

It  is  often  better  to  use  the  instrument  "  differentially,"  i.e.,  Differential 
to  observe  some  neighboring  standard  star  or  stars  of  accurately  use  of.the 
known  position,  soon  before  or  after  the  object  whose  place  is  circie. 
to  be  determined.     We  thus  obtain  the  difference  between  the 
right  ascension  and  declination  of  the  object  observed  and  others 


102  MANUAL   OF   ASTRONOMY 

which  are  accurately  known;  and  in  this  case  slight  errors  in 
the  graduation  and  adjustment  of  the  instrument  affect  the  final 
result  very  little. 

When  a  body  (a  comet,  for  instance)  is  too  faint  to  be  observed 
by  the  telescope  of  the  meridian-circle,  which  is  seldom  very 
powerful,  or  when  it  does  not  come  to  the  meridian  during  the 
night,  we  must  accomplish  our  observation  with  some  instrument 
that  can  pursue  the  object  to  any  part  of  the  heavens.     At 
present  the  equatorial  is  almost  exclusively  used  for  the  purpose. 
Determina-         117,    (2)   By  the  equatorial.     With  this  we  determine  the  posi- 
tion of  posi-    ^ion  of  a  bodv  bv  measuring  the  difference  of  riqht  ascension  and 

tion  by  the  J     J 

equatorial  declination  between  it  and  some  neighboring  star  whose  place 
and  microm-  jg  given  jn  a  star-catalogue,  and,  of  course,  has  been  accurately 
determined  by  the  meridian-circle  of  some  observatory. 

In  measuring  this  difference  of  right  ascension  and  declination 
we  usually  employ  a  micrometer  (Sec.  71)  fitted  with  wires  like 
the  reticle  of  a  meridian-circle.  It  carries  a  number  of  fixed 
wires  which  are  set  accurately  north  and  south  in  the  field  of 
view,  and  these  are  crossed  at  right  angles  by  one  or  more  wires 
which  can  be  moved  by  the  micrometer  screw.  The  difference 
of  right  ascension  between  the  star  and  the  object  to  be  deter- 
mined is  measured  by  clamping  the  telescope  firmly  and  simply 
observing  and  recording  upon  the  chronograph  the  transits  of 
the  two  objects  across  the  wires  that  run  north  and  south;  the 
difference  of  declination,  .by  bisecting  each  object  by  one  of 
the  micrometer  wires  as  it  crosses  the  middle  of  the  field  pf 
view.  The  difference  of  the  two  micrometer  readings  gives  the 
difference  of  declination. 

The  observed!  differences  .must  be  corrected  for ,  refraction 
and  for  the  motion  of  the  body  during  the  time  of  observation. 

The  measurement  ,may  also  be  made  with  the  position  microm- 
eter by  measuring  the  angle  of  position  and  distance  between^ 
tlie  object  and  the  star  of  comparison,  as  it  is  called.' 


PROBLEMS  OF  PRACTICAL  ASTRONOMY      103 

Instead  of  using  a  micrometer  we  may  employ  photography.  Determina- 
For  this  purpose  the  telescope  is  fitted  with  a  plate-holder  in  tlon  of 
place  of  the  eyepiece,  arid  is  accurately  driven  by  clockwork,  photog- 
On  the  sensitive  plate  a  photograph  is  obtained  of  all  the  stars  raPhy- 
in  the  field,  and  also  of  the  object;   and  the  position  of  the 
object  is  afterwards  determined  by  measuring  the  plate.     It  is 
found  that  determinations  of  extreme  accuracy  can  be  made  in 
this  way,  and  the  method  is  rapidly  coming  into  extensive  use. 

EXERCISES 

In  cases  where  corrections  for  refraction  are  required  they  are  to  be 
taken  from  Table  VIII  (Appendix),  taking  into  account  the  temperature 
and  barometric  pressure,  if  given  among  the  data.  If  preferred,  the  student 
may  also  use  Comstock's  formula  (Sec.  82).  The  results  for  example  1 
have  their  corrections  computed  by  the  regular  refraction  tables,  and  the 
approximate  results  obtained  by  the  student  may  differ  from  them  by  a 
considerable  fraction  of  a  second. 

1.  Given  the  following  meridian-circle  observations  on  £  Ursse  Minoris 
at  its  upper  and  lower  culminations,  respectively,  viz. : 

Altitude  55°  48'  06".0,  temperature  30°  F.,  barometer  30.1  inches. 

24°  58'  56".4,  «  25°  F.,          «          30.1      " 

The  nadir  reading  (Sec.  69)  was  270°  01'  06".8  in  both  cases.  Required 
the  latitude  of  the  place  and  the  declination  of  the  star. 

Ans.    Lat.  40°  20'  57".8. 
Dec.  74°  34'  40".l. 

2.  Given  the  meridian  altitude  of  the  sun's  lower  limb  62°  24'  45",  the 
height  of  the  observer's  eye  above  the  sea-level  being  16  feet  (Sec.  77). 

The  sun's  declination  was  +  20°  55'  10"  and  its  semidiameter  15'  47". 
Its  parallax  at  the  observed  altitude  was  5"  and  the  mean  refraction  from 
Table  VIII  may  be  used.  Required  the  latitude  of  the  ship. 

Ans.    +  48°  19'  3". 

^  3.  The  sun's  meridian  altitude  on  a  ship  at  sea  is  observed  to  be  30°  15' 
(after  being  duly  corrected);  the  sun's  declination  at  the  time  is  19°  25' 
south.  What  is  the  ship's  latitude? 

V  4.  How  much  will  a  sidereal  clock  gain  on  a  mean  solar  clock  in  10 
hours  and  30  minutes? 

Ans. 


104  MANUAL   OF   ASTRONOMY 

5.  How  many  times  will  the  second-beats  of  a  sidereal  clock  overtake 
those  of  a  solar  clock  in  a  solar  day  if  they  start  together  ? 

Ans.    236  times. 

6.  At  what  intervals  do  the  coincidences  occur? 

Ans.    6m5.2428. 

7.  Reduce  10  hours  40  minutes  and  25  seconds  of  mean  time  to 
sidereal  time.     (See  Sec.  99.) 

8.  Reduce  10  hours  40  minutes  and  25  seconds  of  sidereal  time  to 
solar  time. 

9.  What  is  the  approximate  sidereal  time  on  July  30  at  10  P.M.  ? 

Solution  by  note  to  Sec.  99.     July  22,  noon  sid.  time         =  8hOOm 

8  days  gain  32 

Sid.  time  at  noon  8h32m 

10  hours      =        sid.   10    If 
Sid.  time  at  10  P.M.     18h33f» 

10.  What  is  the   approximate  sidereal  time  on  October  4  at  7  A.M. 
civil  reckoning? 

11.  In  determining  longitudes  by  telegraph,  will  it  or  will  it  not  make 
any  difference  whether  sidereal  or  solar  clocks  are  used  by  the  observers, 
provided  both  use  the  same  ? 

12.  A  ship  leaving  San  Francisco  on  Tuesday  morning,  October  12, 
reaches  Yokohama  after  a  passage  of  exactly  16  days.     On  what  day  of 
the  month  and  of  the  week  does  she  arrive? 

13.  Returning,  the  same  vessel  leaves  Yokohama  on  Saturday,  Novem- 
ber 6,  and  reaches  San  Francisco  on  Tuesday,  November  23.     How  many 
days  was  she  on  the  voyage  ? 


CHAPTER  V 
THE   EARTH  AS   AN  ASTRONOMICAL  BODY 

Its  Form,  Kotation,  and  Dimensions  —  Mass,  Weight,  and  Gravitation  —  The  Earth's 

Mass  and  Density 

118,  In  a  science  which  deals  with  the  heavenly  bodies  it 
might  seem  at  first  that  the  earth  has  no  place ;  but  certain 
facts  relating  to  it  are  similar  to  those  we  have  to  study  in 

the    case    of   sister   planets,    are    ascertained    by   astronomical  The  earth  an 
methods,  and  a  knowledge  of  them  is  essential  as  a  basis  of  all  astronomi- 

OR!  l)od  v 

astronomical    observations.     In    fact    astronomy,    like    charity,  jn  many 
"begins  at  home,"  and  it  is  impossible  to  go  far  in  the  study  respects. 
of   the  bodies  which    are    strictly    "  celestial "    until  one   has 
acquired    some    accurate    knowledge    of    the    dimensions    and 
motions  of  the  earth  itself. 

119,  The  astronomical  facts  relating  to  the  earth  are  broadly 
these : 

(1)  The  earth  is  a  great  ball  about  7920  miles  in  diameter.          Leading 

(2)  It  rotates  on  its  axis  once  in  twenty-four  sidereal  hours.         astronomi- 

cal facts 

(3)  It  is  not  exactly  spherical,  but  is  flattened  at  the  poles,  the  relating  to 

polar  diameter  being  nearly  27  miles,  or  probably  a  little  more  tne  eartn- 
than  one  three-hundredth  part  less  than  the  equatorial. 

(4)  Its  mean  density  is  between  5.5  and  5.6  as  great  as  that  of 
water,  and  its  mass  is  represented  in  tons  by  6  with  twenty-one 
ciphers  following  (six  thousand  millions  of  millions  of  millions 
of  tons). 

(5)  It  is  flying  through  space  in  its  orbit  around  the  sun  with 
a  velocity  of  about  18\  miles  a  second,  or  nearly  100000  feet  a 
second, — about  thirty-three  times  as  fast  as  the  swiftest  modern 
projectile. 

105 


106 


MANUAL   OF   ASTRONOMY 


Determina- 
tion of  its 
diameter  by 
measuring 
an  arc  of 
meridian 
both  in  miles 
and  in 
degrees. 


I.   ROTUNDITY   AND    SIZE   OF   THE   EARTH 

120.  The  Earth's  Approximate  Form.  —  It  is  not  necessary  to 
dwell  on  the  ordinary  familiar  proofs  of  the  earth's  globularity. 
One,  first  quoted  by*  Galileo  as  absolutely  conclusive,  is  that 
the  outline  of  the  earth's  shadow  seen  upon  the  moon  during  a 
lunar  eclipse  is  such  as  only  a  sphere  could  cast. 

We  may  add,  as  to  the  smoothness  and  roundness  of  the 

earth,  that  if  represented  by  an  18- 
inch  globe,  the  difference  between 
its  greatest  and  least  diameters  would 
be  only  about  TaF  of  an  inch,  the 
highest  mountains  would  project  only 
about  y1^  of  an  inch,  and  the  average 
elevation  of  continents  and  depths  of 
the  ocean  would  be  hardly  greater 
on  that  scale  than  the  thickness  of  a 
film  of  varnish.  Relatively,  the  earth 
is  much  smoother  and  rounder  than 
most  of  the  balls  in  a  bowling-alley. 
121.  The  Approximate  Measure  of 
the  Diameter  of  the  Earth  regarded  as 
a  Sphere.  —  (1)  By  an  arc  of  merid- 
ian. There  are  various  ways  of  deter- 

FIG.  41.  —  Measuring  the  Earth's         .    .  ,  ••         ••.  /.     ,-•_  ,-, 

Diameter  mining  the   diameter   of   the    earth. 

The  simplest  and  best  is  by  measuring 

the  length  of  a  degree.  It  consists  essentially  in  astronomical 
measurements  which  determine  the  distance  between  two  selected 
stations  (several  hundred  miles  apart)  in  degrees  of  the  earth's 
circumference,  combined  with  geodetic  measurements  giving 
their  exact  distance  in  miles  or  kilometers. 

The  astronomical  determination  is  most  easily  made  if  the 
two  stations  are  on  the  same  terrestrial  meridian.  Then,  as  is 
clear  from  Fig.  41,  the  distance  ab  in  degrees  is  simply  the 


THE   EARTH   AS   AN   ASTRONOMICAL   BODY 


107 


Astronom- 
ical work 
consists  in 
measuring 
the  latitudes 
of  the  termi- 
nal stations. 


Geodetic 
work 

consists  in 
measuring 
distance  in 
miles  by 
triangula- 
tion. 


difference  of  latitude  between  a  and  b.  The  latitudes  are  best 
determined  by  zenith-telescope  observations  (Sec.  92),  but  any 
accurate  method  may  be  used. 

The   linear  distance   (in  feet  or  meters)  is  measured  by  a 
geodetic  process  called  triangulation.     It  is  not  practicable  to 
measure  it  with  sufficient  accuracy  directly, 
as  by  simple  "  chaining." 

Between  the  two  terminal  stations  (A 
and  H,  Fig.  42)  others  are  selected,  such 
that  the  lines  joining  them  form  a  com- 
plete chain  of  triangles,  each  station  being- 
visible  from  at  least  two  others.  The 
angles  at  each  station  are  carefully  meas- 
ured, and  the  length  of  one  of  the  sides,  D 
called  the  base,  is  also  measured  with  all 
possible  precision.  It  can  be  done,  and  is 
done,  with  an  error  not  exceeding  an  inch 
in  10  miles.  (B  U  is  the  base  in  the  figure.) 
Having  the  length  of  the  base  and  all  the 
angles,  it  is  then  possible  to  calculate  every 
other  line  in  the  chain  of  triangles  and  to 
deduce  the  exact  north  and  south  distance 
(Ha)  between  H  and  A.  An  error  of  more 
than  three  feet  in  a  hundred  miles  would 
be  unpardonable. 

In  this  way  many  arcs  of  meridian  have 
been  measured  the  average  of  which  (for  they  differ,  because  Result, 
the  earth,  as  we  shall  see,  is  not  quite  spherical)  makes  the 
length  of  a  degree  69.1  miles,  the  mean  circumference  24875 
miles,  and  the  mean  diameter  7918  miles. 

122.  The  ancients  understood  the  principle  of  the  operation 
perfectly.  Their  best  known  attempt  at  a  measurement  of  the 
sort  was  made  by  Eratosthenes  of  Alexandria  about  250  B.C., 
his  two  stations  being  Alexandria  and  Syene  in  Upper  Egypt. 


FIG.  42.  —  Triangulation 


108 


MANUAL   OF   ASTRONOMY 


Method  of  At  Syene  he  observed  that  at  noon  of  the  longest  day  in  summer 
thenes"  there  was  no  shadow  in  the  bottom  of  a  well,  the  sun  being 
then  vertically  overhead.  On  the  other  hand,  the  gnomon  at 
Alexandria  on  the  same  day,  by  the  length  of  the  shadow,  gave 
him  -J0-  of  a  circumference  (7°  15')  as  the  distance  of  the  sun 
from  the  zenith  at  that  place.  This  ^  of  a  circumference  is, 
therefore,  the  difference  of  latitude  between  Alexandria  and 
Syene,  and  the  circumference  of  the  earth  must  be  fifty  times 
the  linear  distance  between  those  two  stations. 


FIG.  43.  —  Curvature  of  the  Earth's  Surface 


The  weak  place  in  his  work  was  the  measurement  of  this  linear  distance 
between  the  two  places.  He  states  it  as  5000  stadia,  without  telling  how  it 
was  measured,  thus  making  the  circumference  of  the  earth  250000  stadia, 
which  may  be  exactly  right ;  for  we  do  not  know  the  length  of  his  stadium, 

nor  does  he  give  any 
account  of  the  means 
by  which  he  measured 
the  distance,  if  he  meas- 
ured it  at  all.  (There 
seem  to  have  been  as 
many  different  stadia 
among  the  ancient  na- 
tions as  there  were  kinds  of  "feet"  in  Europe  at  the  beginning  of  the 
century.) 

The  first  really  valuable  measure  of  an  arc  of  the  .meridian  was  that 
made  by  Picard  in  Northern  France  in  1671,  —  the  measure  which  served 
Newton  so  well  in  his  verification  of  the  idea  of  gravitation. 

Experi-  123.    (2)  The  curvature  of  the  earth's  surface  is  easily  demon- 

mental          strated,  and  an  approximate  estimate  of  its  diameter  obtained, 

exhibition  Jrr 

of  curvature  by  the  following  method.  Erect  upon  a  reasonably  level  plane 
of  earth's  three  rods  in  line,  a  mile  apart,  and  cut  off  their  tops  at  the 
same  level,  carefully  determined  by  a  surveyor's  leveling-instru- 
ment.  It  will  then  be  found  that  the  line  AC  (Fig.  43),  joining 
the  extremities  of  the  two  terminal  rods,  when  corrected  for 
refraction,  passes  about  8  inches  below  B,  the  top  of  the 
middle  rod. 


THE   EARTH   AS   AN   ASTRONOMICAL   BODY  109 

(On  account  of  refraction,  however,  which  curves  the  line  of  Effect  of 
sight  between  A  and  (7,  the  result  cannot  be  made  exact.     The  ^^^  m 
observed  value  of  BD  ranges  all  the  way  from  4.5  to  6.5  inches,  the  apparent 
according  to  the  temperature.)  curvature. 

Suppose  the  circle  ABC  completed,  and  that  E  is  the  point 
on  the  circumference  opposite  B,  so  that  BE  equals  the  diameter 
of  the  earth  (=2.K). 

By  geometry,  BD:BA  =  BA:  BE,  or  2  R,  Computa- 

2  tion  of 


whence 

diameter 


from  such 

Now  BA  is  1  mile,  and  BD  =  8  inches,  or  |  of  a  foot,  or  y-J^  observa- 
of  a  mile.  tion8' 

Hence,  2  R  (the  earth's  diameter)  =  7920  miles,  —  a  very  fair 
approximation. 

II.    THE   ROTATION   OF   THE  EARTH 

124.  Probable  Evidence  of  the  Earth's  Rotation.  —  At  the  time 
of  Copernicus  the  only  argument  he  could  bring  in  favor  of 
the  earth's  rotation  was  that  this  hypothesis  was  much  more 
probable  than  the  older  one  that  the  great  heavens  themselves 
revolved.  All  the  phenomena  then  known  would  be  sensibly 
the  same  on  either  supposition.  The  apparent  diurnal  motion  Probability 
of  the  heavenlv  bodies  can  be  f  ullv  accounted  for  within  the  of  the 

J  J  earth's 

limits  of  observation  then  possible,  either  by  supposing  that  rotation. 
the  stars  are  actually  attached  to  an  immense  celestial  sphere 
which  turns  around  daily,  or  that  the  earth  itself  rotates  upon 
an  axis;  and  for  a  long  time  the  latter  hypothesis  seemed  to 
most  people  less  probable  than  the  older  and  more  obvious  one. 

A  little  later,  after  the  invention  of  the  telescope,  analogy 
could  be  adduced;  for  with  the  telescope  we  can  see  that  the 
sun,  moon,  and  many  of  the  planets  are  rotating  globes. 

Within  the  last  century  it  has  become  possible  to  adduce 
experimental  proofs  which  go  still  further  and  absolutely 


110 


MANUAL   OF   ASTRONOMY 


Experi- 
mental 
proof  of 
the  earth's 
rotation  by 
the  Foucault 
pendulum. 


demonstrate  the  earth's  rotation.     Some   of  them  even  make 
it  visible. 

125.  Foucault's  Pendulum  Experiment. — Among  these  experi- 
mental proofs  the  most  impressive  is  the  pendulum  experiment, 
devised  and  first  executed  by  Foucault  in  1851.  From  the 
dome  of  the  Pantheon  in  Paris  he  hung  a  heavy  iron  ball  about 
a  foot  in  diameter  bv  a  wire  more  than  200  feet  long  (Fig.  44). 

A  circular  rail  some  12  feet 
across,  with  a  little  ridge  of  sand 
built  upon  it,  was  placed  in  such 
a  way  that  a  pin  attached  to  the 
swinging  ball  would  just  scrape 
the  sand  and  leave  a  mark  at 
each  vibration.  To  put  the  ball 
in  motion  it  was  drawn  aside  by 
a  cotton  cord  and  left  for  hours 
to  come  absolutely  to  rest ;  then 
the  cord  was  burned  and  the 
pendulum  started  without  jar  to 
swing  in  a  true  plane. 

But  this  plane  at  once  began 
apparently  to  deviate  slowly  to- 
wards the  right,  in  the  direction 
of  the  hands  of  a  watch,  and 
the  pin  on  the  pendulum  ball  cut 
the  sand  ridge  in  a  new  place 
at  each  swing,  shifting  at  a  rate  which  would  carry  it  completely 
around  in  about  thirty-two  hours  if  the  pendulum  did  not  first 
come  to  rest.  In  fact,  the  floor  of  the  Pantheon  was  really  and 
visibly  turning  under  the  plane  of  the  vibrating  pendulum. 

Fig.  45  is  copied  from  a  newspaper  of  that  date  and  shows 
the  actual  appearance  of  the  apparatus  and  its  surroundings. 
The  experiment  created  great  enthusiasm  at  the  time  and  has 
since  been  frequently  repeated. 


FIG.  44. —  Foucault's  Pendulum 
Experiment 


THE   EARTH   AS   AST   ASTRONOMICAL   BODY 


111 


126.  Explanation  of  the  Foucault  Experiment.  —  The  approxi- 
mate theory  of  the  experiment  is  very  simple.  A  swinging 
pendulum,  suspended  so  as  to  be  equally  free  to  swing  in  any 
plane  (unlike  the  common  clock  pendulum  in  this  freedom),  if 
set  up  at  the  pole  of  the  earth,  would  appear  to  shift  completely 
around  in  twenty-four  hours.  Really  in  this  case  the  plane  of 
vibration  remains  unchanged  while  the  earth  turns  under  it. 
This  can  easily  be  understood  by  setting  up  on  a  table  a  similar 
apparatus,  consisting  of  a 
ball  hung  from  a  frame  by 
a  thread,  and  then,  while 
the  ball  is  swinging,  turn- 
ing the  table  around  upon 
its  casters  with  as  little  jar 
as  possible.  The  plane  of 
the  swing  will  remain  un- 
changed by  the  motion  of 
the  table. 

It  is  easy  to  see,  more- 
over, that  at  the  earth's 
equator  there  will  be  no 
such  tendency  to  shift; 
while  in  any  other  latitude 

„  ...    .        .    ,  FIG.  45.  —  Foucault's  Pendulum  in  the 

the  effect  will  be  interme-  Pantheon 

diate  and  the  time  for  the 

pendulum  to  complete  the  revolution  in  its  plane  will  be  longer 

than  at  the  pole= 

The  northern  edge  of  the  floor  of  a  room  in  the  northern 
hemisphere  is  nearer  the  axis  of  the  earth  than  is  its  southern 
edge,  and  therefore  is  carried  more  slowly  eastward  by  the 
earth's  rotation.  Hence,  the  floor  must  "skew"  around  con- 
tinually, like  a  postage-stamp  gummed  upon  a  whirling  globe, 
anywhere  except  at  the  globe's  equator.  A  line  drawn  on 
the  floor,  therefore,  continually  shifts  its  direction,  and  a  free 


Why  the 
free  pendu- 
lum appears 
to  shift  its 
plane.    Rate 
of  shift  at 
the  pole. 


No  shift  at 
the  equator 


Effect  at 
inter- 
mediate 
latitudes. 


112  MANUAL   OF   ASTRONOMY 

pendulum,  set  at  first  to  swing  along  such  a  line,  must  appar- 
ently deviate  at  the  same  rate  in  the  opposite  direction. 

It  can  be  proved  (see  General  Astronomy,  Arts.  140,  141) 
that  the  hourly  deviation  of  a  Foucault  pendulum  equals  15° 
multiplied  by  the  sine  of  the  latitude.  In  the  latitude  of  New 
York  it  is  not  quite  10°  an  hour. 

In  the  northern  hemisphere  the  plane  of  vibration,  as  already 
stated,  moves  around  with  the  hands  of  a  watch.  In  the 
southern  the  motion  is  reversed. 

127.  There  are  various  other  demonstrations  of  the  earth's 
rotation  which  we  merely  mention,  referring  to  the  author's 
General  Astronomy  for  their  discussion : 

(a)  By  the  gyroscope,  an  experiment  also  due  to  Foucault. 

(b)  By  the  slight  eastward  deviation  of  bodies  in  falling  from  a 
height.     This  deviation  is,  of  course,  zero  at  the  pole  and  a  maxi- 
mum at  the  equator ;  it  varies  as  the  cosine  of  the  latitude,  other 
things  being  equal,  and  amounts  to  about  one  inch  in  a  fall  of 
500  feet  for  a  station  in  latitude  50°.     The  idea  of  the  experi- 
ment is  due  to  Newton,  but  its  execution  has  been  carried  out 
only  during  the  past  century,  by  several  European  observers. 

If  the  earth  were  strictly  spherical,  and  if  gravity  were 
directed  to  its  center,  there  would  also  be  a  slight  deviation 
towards  the  equator.  But  Laplace  has  shown  that,  as  things 
are,  no  sensible  deviation  of  that  kind  takes  place. 

(c)  By  the  deviation  of  projectiles  to  the  right  in  the  northern 
hemisphere,  to  the  left  in  the  southern: 

(d)  By  various  phenomena  of  meteorology  and  physical  geog- 
raphy, —  such   as   the    direction   of  the   trade    and  anti-trade- 
winds  and  of  the  great  ocean  currents,  and  the  counter-clockwise 
revolution  of  cyclones  in  the  northern  hemisphere,  reversed  in 
the  southern. 

It  might  at  first  seem  that  the  rotation  of  the  earth  once  a 
day  is  not  a  very  rapid  motion,  but  a  point  on  the  equator 
travels  nearly  1000  miles  an  hour,  or  about  1500  feet  a  second. 


THE   EARTH   AS   AN   ASTRONOMICAL   BODY          113 

128.   Invariability  of  the  Earth's  Rotation It  is  a  question 

of  great  importance  whether  the  day  ever  changes  its  length,  Question  as 
for  if  it  does  our  time  unit  is  not  a  constant.     Theoretically,  j^™™" 
some  change  is  almost  inevitable.     The  friction  of  the  tides  earth's 
and  the  deposit  of  meteoric  matter  on  the  earth's  surface  both  rotation- 
tend  to  retard  its  rotation ;  on  the  other  hand,  the  earth's  loss 
of  heat  by  radiation,  and  its   consequent  shrinkage,  tend  to 
accelerate  it  and  to  shorten  the  day.     Then  geological  causes 
act,  some  one  way  and  some  the  other. 

At  present  we  can  only  say  that  the  change  which  may  have 
occurred  since  astronomy  has  been  accurate  is  too  small  to  be  Certain  that 
surely  detected.     The  day  is  certainly  not  longer  or  shorter  by  change» lf 
-^  part  of  a  second  than  it  was  in  the  days  of  Ptolemy,  and  been 
probably  it  has  not  altered  by  y-^-  of  a  second.     The  test  is  extremely 
found  in  comparing  the  times  at  which  celestial  phenomena, 
such  as  eclipses,  transits  of  Mercury,  etc.,  have  occurred  during 
the  range  of  astronomical  history. 

Professor   Newcomb's    investigations    in   this    line    make  it 
highly  probable,  however,  that  the  length  of  the  day  has  not  Some  indi- 
been   quite   constant  during    the    last  150   years.     There   are  ^tl1^sof 
suspicious  indications  that  Greenwich  noon  has,  at   irregular  acceiera- 
intervals  of  from  thirty  to  fifty  years,  sometimes  come  too  early  * 
by  as  much  as  four  or  five  seconds,  and  at  other  times  fallen  as  tions. 
much  behind.     Astronomers  are  somewhat  anxious  on  the  sub- 
ject, because  if  the  earth's  rotation  should  turn  out  to  be  capri- 
ciously changeable  in  any  sensible  degree,  it  would  compel  us 
to  look  for  some  new  and  independent  unit  of  time. 


EFFECTS  OF  THE  EARTH'S  ROTATION  UPON  GRAVITY  ON  THE 
EARTH'S  SURFACE  AND  UPON  THE  EARTH'S  FORM 

129.   Centrifugal  Force  due  to  the  Earth's  Rotation.  —  As  the 

earth  rotates  on  its  axis  every  particle  of    its  surface  is.  sub- 
jected to  a  "  centrifugal  force  "  directed  perpendicularly  away 


114 


MANUAL   OF   ASTRONOMY 


Centrifugal    from  the  axis,  and  this  force,  (7,  depends  upon  the  velocity  of 
force  due       ^  particle  an(j  the  radius  of  the  circle  in  which  it  moves. 

to  earth  s 

rotation  at         According  to  a  familiar  formula,  this  centrifugal  force,  (7, 

the  equator  y  2 

equals  ^  of  equals  —  -  (Physics,  p.  63).     An  equivalent  formula,  often  more 

gravity.  -^ 

convenient,  is  C  —  — — — ,  since  F  equals  2  TrR,  the  circumfer- 
ence of  the  circle,  divided  by  T,  the  time  of  revolution.  This 
gives  C  as  an  "  acceleration  "  (in  feet  per  second),  just  as  gravity 
is  given  by  g. 

The  equatorial  radius  of  the  earth  being  20  926202  feet, 
and  the  time  of  revolution,  or  the  sidereal  day,  being  86167 

mean  solar  seconds,  we  find  C  =  0.1112 
feet  per  second,  or  1.334  inches  per 
second.  This  is  ^-J-g  part  of  g,  which 
is  386  inches  per  second.  At  the 
earth's  equator,  therefore,  C  equals 

sio"  9- 

Since  centrifugal  force  varies  with 

the  square  of  the  velocity,  and  289 
is  the  square  of  17,  it  appears  that  if 
the  earth  revolved  seventeen  times  as 

swiftly,  keeping  its  present  size  and  form  (an  impossible  suppo- 
sition), bodies  at  the  equator  would  lose  all  their  weight;  and 
if  the  speed  were  increased  beyond  that  point,  everything  on 
the  surface  there  would  fly  off  unless  fastened  down. 

At  any  other  latitude,  assuming  the  earth  to  be  spherical, 
which  is  sufficiently  accurate  for  our  present  purpose,  the 
radius  of  the  circle  described  by  M  (Fig.  46)  is  MN,  which 
equals  R  cos  </>;  i.e.,  at  any  latitude  the  centrifugal  force  c 
equals  C  cos  <£  =  -^-3  g  X  cos  $,  becoming,  therefore,  zero  at 
the  pole. 

130,  Effects  of  Centrifugal  Fof  ce'  on  Gravity.  —  At  the  equator 
the  whole  centrifugal  force"  is  opposed  to  gravity,'  so  that  bodies' 


A  rotation 
seventeen 
times  as 
rapid  would 
cause  bodies 
to  fly  off 
from  the 
earth's 
surface. 


Centrifugal 
force  at  any 
latitude  is 
propor- 
tional to  the 
cosine  of 
tlie  latitude. 


FIG.  46.  —  Centrifugal  Force 
Caused  by  Earth's  Rotation 


THE   EARTH   AS   AN   ASTRONOMICAL   BODY 


115 


there  weigh  on  this  account  ^-g  less  (weighed  by  a  spring- 
balance)  than  they  would  if  the  earth  did  not  rotate;  but  the 
direction  of  gravity  is  not  altered.  Elsewhere,  except  at  the 
pole  itself,  both  the  amount  and  direction  of  gravity  are 
affected. 

(a)  Diminution  of  G-ravity.     Referring  to  the  figure,  we  see 
that  the  centrifugal  force  MT,  or  c,  is  resolvable  into  two  compo- 
nents, of  which  MR  acts  radially  in  direct  opposition  to  gravity 
and  equals  MT  X  cos  TMR  =  c  cos  <f>  =  C  cos2  </>. 

(b)  Change  of  Direction  of  G-ravity.     MS,  the  other  compo- 
nent of  e,   acts   horizontally  towards   the  equator  and  equals 
C  cos  <f)  sin  (j>  =  l-  C  sin  2  $. 

It  acts  to  make  the  plumb-line 
hang  away  from  the  radius 
towards  a  point  between  0 
and  Q. 

In  latitude  45°  this  hori- 
zontal force  has  its  maximum 
and  is  about  ^^  part  of 
the  whole  force  of  gravity, 
causing  the  plumb-line  to 
deviate  towards  the  equator  FlG>  4T 
about  Qf  from  the  radius. 

If  the  earth's  surface  were  spherical,  this  horizontal  force 
would  make  every  loose  particle  tend  to  slide  towards  the  equa- 
tor, and  the  water  of  the  ocean  would  so  move.  As  things 
actually  are,  the  surface  of  the  earth  has  already  arranged  itself 
accordingly,  and  the  earth  bulges  at  the  equator  just  enough  to 
correct  this  sliding  tendency. 

This  effect  of  the  earth's  rotation  on  its  form  is  well  illustrated  by  the 
familiar  little  .piece  of  apparatus'  shown  in  Fig.  47. 

If  the  earth's  rotation  were  to  cease,  the  Mississippi  River  would  at  once 
Have  its  course  Reversed,  since  its  mouth  is  several  thousand  feet  farther 
from  the  center  of  the  earth  than  are  its  sources* 


Effect  of  Earth's  Rotation  on  its 
Form 


Centrifugal 
force 

resolvable 
into  two 
components 


Vertical 
component 
opposed  to 
gravity. 

Horizontal 
component 
affects 
direction  of 
gravity. 


Maximum  at 
45°  latitude 


116  MANUAL   OF   ASTROiVOMY 

131.   Gravity  is  not  simply  gravitation,  —  the  attraction  of  the 
Distinction     earth  for  a  body  upon  its  surface,  —  but  is  the  resultant  of 


between         ^-g  aftraction  combined  with  the  centrifugal  force  at  the  point 

gravity  and 

gravitation,  of  observation,  as  above  explained.  It  is  this  resultant  force 
which  determines  the  weight  of  a  body  at  rest  or  its  velocity 
and  direction  when  falling.  Only  at  the  equator  and  poles  is 
gravity  directed  towards  the  center  of  the  earth.  Surfaces  of 
level  are,  on  hydrostatic  principles,  necessarily  everywhere  per- 
pendicular to  gravity,  and  are  therefore  not  spheres  around  the 
earth's  center,  but  spheroids  flattened  at  the  poles. 

132.   The  Earth's  Form.  —  There  are  three  ways  of  determin- 

ing the  form  of  the  earth  :  First,  by  geodetic  measurement  of 

distances  upon  its  surface  in  connection  with  the   astronomical 

Classifica-      determination  of  the  points  of  observation.     This  gives  not  only 

tion  of  the  form  but  also  the  linear  dimensions  in  miles  or  kilometers. 

methods  for  . 

determining        Second,  by  observing  the  varying  force  of  gravity  at  points 
accurately      jn  different  latitudes,  —  observations  which  are  made  by  means 
the  earth  °      °^  a  pendulum  apparatus  of  some  kind  and  determine  only  the 
form  but  not  the  size  of  the  earth. 

Third,  by  means  of  purely  astronomical  phenomena,  known  as 
precession  and   nutation  (to  be  treated   of  hereafter),  and  by 
certain  irregularities  in  the  motion  of  the  moon.     Observations 
of  the  occultations  of  stars  at  widely  distant  stations  can  also 
be  utilized  for  the   same  purpose.     These   methods,  like  the 
pendulum  method,  give  only  the  form  of  the  earth. 
Definition  of       It  is  usual  to  characterize  the  form  of  the  earth  by  its  oblate- 
obiateness,     ne§8^  or  ellipticity,  though  the  latter  term  is  rather  objectionable 
ticity.  on  account  of  the  danger  of  confounding  it  with  eccentricity. 

The  oblateness  (O)  is  the  fraction  obtained  by  dividing  the 
difference  between  the  polar  and  equatorial  semidiameters  by 

the  equatorial,  i.e.,  O  =  —  -  --     In  the  case  of  the  earth  this  is 

A 

about  g-l-Q,  but  determinations  by  different  methods  range  all 
the  way  from  about  -^^  to 


THE   EARTH   AS   AN   ASTRONOMICAL   BODY          117 

The  eccentricity  of  an  ellipse  is  — — ,  and  is  always  a  much  larger 

A. 

quantity  than  the  oblateness,  or  ellipticity.     In  the  case  of  the  earth's 
meridian  it  is  about  r^j*     Its  symbol  in  astronomy  is  usually  e. 

133.   Geodetic  Method,  by  which  Dimensions  of  the  Earth  as  Geodetic 
well  as  its  Form  are  determined.  —  The   method   in   its  most  methodof 

determining 

convenient  shape  consists  essentially  in  the   measurement  of  the  earth's 

two   (or   more)   arcs   of  meridian  in  widely   different  latitudes.  dimensions 

and  form. 

These  measurements  are  effected  by  the  same  combination  of 
astronomical  and  geodetic  operations  already  described  for  the 
measurement  of  a  single  arc  (Sec.  121).  More  than  twenty 
have  thus  far  been  meas- 
ured in  various  parts  of 
the  earth.  The  two 
longest  are  the  great 
Russo-Scandinavian  arc, 
extending  from  Hammer- 
fest  to  the  mouth  of  the 
Danube,  and  the  Indian 
arc  of  practically  equal 

_  .  _  FIG.  48.  —  Length  of  Degrees  in  Different 

length,  reaching  from  the  Latitudes 

Himalayas  to  the  south- 
ern extremity  of  the  great  peninsula.     These  are  both  between 
25°  and  30°  long ;  few  of  the  others  exceed  10°. 

From  these  measures  it  appears  in  a  general  way  that  the 
higher  the  latitude  the  greater  the  length  of  each  astronomical 
degree.     Thus,  near  the  equator  a  degree  has  been  found  to  be 
362800  feet  in  round  numbers,  while  in  Northern  Sweden,  in  Length  of 
latitude  66°,  it  is  365800  feet.     In  other  words,  the  earth's  ^^ 
surface  is  flatter  near  the  poles,  as  illustrated  by  Fig.  48.     It  is  ical  latitude 
necessary  to  travel  about  3000  feet  farther  in   Sweden  than  s™&test 

^  near  tne 

in  India  to  increase  the  latitude  by  one  degree,  as  measured  by  poie. 
the  elevation  of  the  celestial  pole. 


118  MANUAL   OF   ASTRONOMY 

The  following  little  table  gives  the  length  of  a  degree  of  the 
meridian  in  certain  latitudes : 

At  the  equator  one  degree  =  68.704  miles. 

At  lat.  20°  «  «  =  68.786  " 

"  «  40°  «  «  =  68.993  " 

«  «  45°  «  «  =  69.054  « 

"  "  60°  «  "  =  69.230  " 

«  «  80°  «  «  =  69.386  « 

At  the  pole  «  «  -  69.407      " 

It  will  be  understood,  of  course,  that  the  length  of  a  degree 
at  the  pole  is  obtained  by  "  extrapolation  "  from  the  measures 
made  in  lower  latitudes. 

The  difference  between  the  equatorial  and  polar  degree  of 
latitude  is  more  than  3500  feet,  while  the  probable  error  of 
measurement  cannot  exceed  more  than  three  or  four  feet  to 
the  degree. 

134,  The  deduction  of  the  exact  form  of  the  earth  from 
Difficulty  of  such  measurements  is  an  abstruse  problem.  Owing  to  errors 
deducing  Q£  okservation,  and  to  local  deviations  in  the  direction  of 

consistent 

results  from  gravity  due  to   unevenness   of  surface   and  variation   of  den- 
the  observa-  s^y  jn  ^e   rocks  near  the  station,  the  different  arcs  do  not 

tions.  J 

give  strictly  accordant  results,  and  the  best  that  can  be  done 
is  to  find  the  result  which  most  nearly  satisfies  all  the  obser- 
vations. 

According  to  the  determination  of  Colonel  Clarke,  for  a  long 
time  at  the  head  of  the  English  Ordnance  Survey,  the  dimen- 
sions of  the  "  spheroid  of  1866  "  (which  is  still  accepted  by  our 
Coast  and  Geodetic  Survey  as  the  basis  of  all  its  calculations) 
are  as  follows: 

The  earth's  Equatorial  radius  (^4)6  378206.4  meters  =  3963.307  miles, 

dimensions  Polar  radius  (B)  6  356583.8       «  =  3949.871       « 

according  to  Difference  21622.6       «  =      13.436      « 

Colonel  1 

Clarke.  .       13'436  I 

Oblateness  3963.307  =     295.0         « 


THE   EARTH   AS  AN   ASTRONOMICAL   BODY          119 

These  numbers  are  likely  to  be  in  error  as  much,  perhaps,  as 
100  meters,  and  possibly  somewhat  more;  they  can  hardly 
be  300  meters  wrong.1 

The  oblateness  —  -  —  comes  out  3^5;  ^u^  a  comparatively 


small  change  in  either  the  equatorial  or  polar  radius  would 
change  the  295  by  some  units. 

At  present  the  distance  from  a  point  on  the  earth's  surface  Uncertainty 
(say  the  observatory  at  Washington)  to  any  point  in  the  oppo-  ^t^resent 
site  hemisphere  (say  the  observatory  at  the  Cape  of  Good  Hope) 
is  uncertain  by  fully  1000  feet. 

The  deviation  of  the  earth's  form  from  a  true  sphere  is  due 
simply  to  its  rotation,  and  might  have  been  cited  as  proving  it. 
As  already  shown,  the  centrifugal  force  caused  by  the  rotation 
modifies  the  direction  of  gravity  everywhere  except  at  the 
equator  and  the  poles,  and  the  surface  therefore  necessarily 
takes  the  spheroidal  form. 

135.   Arcs  of  longitude  are  also  available  for  determining  the  Availability 
earth's  form  and  size.     On  an  oblate  or  orange-shaped  spheroid  ^^^ 
(since   the  surface  lies  wholly  within   the    sphere  which   has  or  of  any 
the  same  equator)  the  degrees  of  longitude  are  evidently  every-  extens|ve 
where  shorter  than  on  the  sphere,  the  difference  being  greatest  astronom- 
at  a  latitude  of  45°,  and  from  this  difference  when  actually  ical  surveys 
determined  the  oblateness  can  be  computed. 

In  fact,  arcs  in  any  direction  between  stations  of  which  loth  the 
latitude  and  longitude  are  known  can  be  utilized  for  the  purpose  ; 
and  thus  all  the  extensive  geodetic  surveys2  that  have  been 

1  For  Clarke's  spheroid  of  1878,  see  Appendix. 

2  It  is  extremely  improbable  that  the  actual  geoid  (the  regular  geometrical  sur- 
face which  most  nearly  fits  the  surface  of  the  earth)  is  a  perfect  spheroid,  or  even  a 
perfect  ellipsoid  of  three  axes.  The  local  and  continental  irregularities  are  so  great 
that  it  seems  likely  that  it  will  be  found  best  to  adopt  some  one  of  the  already 
computed  spheroids  as  a  final  "  surface  of  reference,"  and  hereafter  to  investi- 
gate and  tabulate  the  local  deviations  from  this  as  a  base,  rather  than  to  com- 
pute a  new  set  of  spheroid  elements  for  every  accession  of  new  geodetic  data. 


120 


MANUAL   OF    ASTRONOMY 


vations. 


Loss  of 
weight  at 
equator  is 
lie  as  com- 
pared with 
weight  at 
the  pole. 


made  by  different   countries   contribute  to  our  knowledge   of 

the  earth's  dimensions. 

Determina-        136.   Determination  of  the  Earth's  Form  by  Pendulum  Experi- 
tion  of  form   ments  an(j  purely  Astronomical  Observations.  —  Since  t,  the  time 

by  pendu- 

of  vibration  of  a  pendulum  (Physics,  p.  68),  equals  «•  \_,  we 

I  9 

have  g  —  iP  -%>  and  can  therefore  measure  the  variations  of  g,  the 

force  of-  gravity,  at  different  parts  of  the  earth  by  using  a  pendu- 
lum of  invariable  length  and  determining  its  time  of  vibration  at 
each  station.  Extensive  surveys  of  this  sort  have  been  made  and 
are  still  in  progress ;  and  it  is  found  from  them  that  the  force  of 
gravity  at  the  pole  exceeds  that  at  the  equator  by  about  T^. 
In  other  w^ords,  a  man  who  weighs  190  pounds  at  the  equator 
(weighed  by  a  spring-balance)  would  weigh  191  at  the  pole. 

The  centrifugal  force  of  the  earth's  rotation  accounts  for  about 
one  pound  in  289  of  this  difference ;  the  remainder  (about  one 
pound  in  555)  has  to  be  accounted  for  by  the  difference  between 
the  distances  from  the  poles  and  from  the  equator  to  the  center 
of  the  earth.  At  the  pole  a  body  is  more  than  13  miles  nearer 
the  center  of  the  earth  than  at  the  equator,  and  as  a  conse- 
quence the  earth's  attraction  upon  it  is  greater.  The  difference 
of  gravity  between  pole  and  equator  depends,  however,  not 
only  on  the  difference  of  distance  from  the  center  of  the  earth, 
but  partly  on  the  distribution  of  density  within  the  globe. 

Assuming  what  is  probable,  that  the  strata  of  equal  density 
are  practically  concentric,  Clairaut  has  proved  that  for  any  planet 
ciairaut's  of  small  oblateness, 

equation.  \l  =  1^  C  —  W, 

in  which  C  equals  the  centrifugal  force  at  the  planet's  equator 
and  W  the  diminution  of  gravity  between  pole  and  equator; 
i.e.,  for  the  earth, 


x 


259 


-     '  which  gives  n  = 


THE   EARTH   AS   AN   ASTRONOMICAL   BODY          121 

The  purely  astronomical  methods  for  determining  the  form  of 
the  earth  indicate  a  slightly  smaller  oblateness  of  about  -gfa.  Result  of 
They  depend  upon  precession  and  nutation  (Sees.  168  and  170)  ^^a*st 
and  upon  certain  irregularities  in  the  motion  of  the  moon ;  but  methods, 
their  discussion  lies  quite  beyond  our  scope. 

From  a  combination  of  all  the  available  data  of  every  kind, 
Harkness  (1891)  gives  as  his  final  result  for  the  oblateness, 


a  = 


300.2  ±3.0 


137.  Station  Errors.  —  If  the  latitudes  of  all  the  stations  in 
a  triangulation  as  determined  by  astronomical  observations  are 
compared  with  their  differences  of  latitude  as  deduced  from  station 
the  geodetic   operations,   we   find  discrepancies   by  no  means  errorsdue 
insensible.     They  are  far  beyond  all  possible  errors  of  observa-  distribution 
tions  and  are  due  to  irregularities  in  the  direction  of  gravity,  of  matter  in 
which  depend  upon  the  variations  in  density  and  form  of  the  eartht 
crust  of  the  earth  in  the  neighborhood  of  the  station.     Such 
irregularities  in  the  direction  of  gravity  displace  the  astronom- 
ical zenith  of  the  station.      They  are  called  station  errors  and 

can  be  determined  only  by  a  comparison  of  astronomical  posi- 
tions by  means  of  geodetic  operations.  According  to  the  Coast 
Survey,  station  errors  average  about  l;/.5  in  the  eastern  part 
of  the  United  States,  affecting  both  the  longitudes  and  lati- 
tudes of  the  stations  and  the  astronomical  azimuths  of  the 
lines  that  join  them.  Station  errors  of  from  4"  to  6"  are  not 
very  uncommon,  and  in  mountainous  countries  these  deviations 
occasionally  rise  to  30"  or  40". 

138.  Astronomical,  Geographical,  and  Geocentric  Latitudes.—     Astronom- 
(1)  The  astronomical  latitude  of  the  station  is  that  actually  ica1'  se°- 
determined  by  astronomical  observations,  —  simply  the  observed  an(j  geocen- 
altitude  of  the  pole.  triciatitudes 

(2)  The  geographical   latitude   is  the  astronomical   latitude  distin. 
corrected  for  station  error.     It  may  be   defined  as  the   angle  guisned. 


122 


MANUAL   OF    ASTRONOMY 


Geocentric 
latitude  and 
the  angle  of 
the  vertical. 


Inverse 
relation 
of  geocentric 
degrees  to 
astro- 
nomical. 


formed  with  the  plane  of  the  equator  by  a  line  drawn  from  the 
place  perpendicular  to  the  surface  of  the  standard  spheroid  at 
that  station.  Its  determination  involves  the  adjustment  and 
evening  off  of  the  discrepancies  between  the  geodetic  and  astro- 
nomical results  over  extensive  regions.  The  geographical 
latitudes  (sometimes  called  topographical)  are  those  used  in  con- 
structing an  accurate  map. 

For  most  purposes,  however,  the  distinction  between  astronomical  and 
geographical  latitudes  may  be  neglected,  since  on  the  scale  of  an  ordinary 
map  the  station  errors,  amounting  at  most  to  a  few  hundred  feet,  would  be 
entirely  insensible. 

(3)  G-eocentric  Latitude.  While  the  astronomical  latitude  is 
the  angle  between  the  plane  of  the  equator  and  the  direction  of 
gravity  at  any  point,  the  geocentric  lati- 
tude, as  the  name  implies,  is  the  angle, 
at  the  center  of  the  earth,  between  the 
plane  of  the  equator  and  a  line  drawn 
from  the  observer  to  that  center;  which 
line  evidently  does  not  coincide  with 
the  direction  of  gravity,  since  the  earth 
is  not  spherical. 

In  Fig.  49  the  angle  MNQ  is  the  astro- 
nomical latitude  of  the  point  M  (it  is 

also  the  geographical  latitude,  provided  the  station  error  at  that 
point  is  insensible),  and  MOQ  is  the  geocentric  latitude. 

The  angle  ZMZ',  the  difference  of  the  two  latitudes,  is  called 
the  angle  of  the  vertical  and  is  about  11'  in  latitude  45°. 

Geocentric  degrees  are  longest  near  the  equator,  in  precise 
contradiction  to  the  astronomical  degrees  ;  and  it  is  worth  notic- 
ing that  if  we  form  a  table  like  that  of  Sec.  133,  giving  the 
length  of  each  degree  of  geographical  latitude  from  the  equator 
to  the  pole,  the  same  table,  read  backwards,  gives  the  length  of 
the  geocentric  degrees  without  sensible  inaccuracy;  i.e.,  at  any 
Distance  from  the  pole  a  degree  of  geocentric  latitude  has  within 


0 


N 


Q 


FIG.  49.  —  Astronomical  and 
Geocentric  Latitude 


THE   EARTH   AS   AN   ASTRONOMICAL   BODY          123 

a  few  inches  just  the  same  length  as  the  astronomical  degree  at 
the  same  distance  from  the  equator. 

Geocentric  latitude  is  employed  in  certain  astronomical  cal- 
culations, especially  such  as  relate  to  the  moon  and  eclipses,  in 
which  it  becomes  necessary  to  "reduce  observations  to  the 
center  of  the  earth." 

139,  Surface  and  Volume  of  the  Earth.  —  The  earth  is  so 
nearly  spherical  that  we  can  compute  its  surface  and  volume  (or 
"bulk")  with  sufficient  accuracy  by  the  formulae  for  a  perfect 
sphere,  provided  we  put  the  earth's  mean  semidiameter  for 
radius  in  the  formulae. 

This  mean  semidiameter  of  an  oblate  spheroid  is  not  — — ,  Meansemi- 

9  /»  _|_  A  diameter  of 

but  -— — ,  because  if  we  draw  through  the  earth's  center  three  an  oblate 

o  spheroid. 

axes  of  symmetry  at  right  angles  to  each  other,  one  only  will 
be  the  axis  of  rotation,  and  both  the  others  will  be  equatorial 
diameters. 

The  mean  radius  r  of  the  earth  thus  computed  is  3958.83 
miles ;  its  surface  (4  irr2)  is  196  944000  square  miles,  and  its 
volume  TiT3)  260000  million  cubic  miles,  in  round  numbers. 


III.  THE  EARTH'S  MASS  AND  DENSITY 

140.    Definition  of  Mass.  —  The  Mass  of  a  body  is  the  quantity  Definition 
of  matter  in  it,  i.e.,  the  number  of  tons,  pounds,  or  kilograms  of  ( 
material  which  it  contains,  —  the  unit  of  mass  being  a  certain 
arbitrary  body  which  has  been  selected  as  a  standard.     A  "  kilo- 
gram," for  instance,  is  the  amount  of  matter  contained  in  the 
block  of  platinum  which  is  preserved  as  the  standard  at  Paris. 
The   mass  of  a  body  in  the  last  analysis  is  measured  by  its  its  relation 
inertia,  i.e.,   by  the  force   required  to  give  the   body   a   certain  to  force' 
velocity  in  a  given  time. 

Mass  must  not  be  confounded  with  "  volume "  or  "  bulk," 
which  is  simply  the  amount  of  space  (cubic  units)  occupied  by 


124  MANUAL   OF   ASTRONOMY 

Distinction     the  body.     A  bushel  of  coal  has  the  same  volume  as  a  bushel 
between        Qf  feathers,  but  its  mass  is  immensely  greater. 

mass,  on  one 

hand,  and          Nor   must   mass  be   confounded  with   "  weight,"   which   is 
volume  and    simply  the  force  (push  or  pull)  which  urges  the  body  towards 

weight,  on         ,  ,         T  ,  ,  -,. 

the  other.  the  earth.  It  is  true  that  under  ordinary  terrestrial  conditions 
the  mass  of  a  body  and  its  weight  are  proportional  to  each 
other  and  numerically  equal.  A  mass  of  ten  pounds  weighs 
(very  nearly)  ten  pounds  anywhere  on  the  earth's  surface,  but 
the  word  "pound"  in  the  two  parts  of  the  sentence  means  two 
entirely  different  things  ;  the  pound  of  "  mass  "  and  the  pound 
of  "  force  "  (stress)  are  as  distinct  as  a  "  beam  "  of  timber  from 
a  "  beam  "  of  sunlight. 

141.   Mass  and  Force  (Stress)  distinguished.  —  This  identity 
of  names  for  the  units  of  mass  and  force  is  on  many  accounts 

Ambiguities   unfortunate,  causing  much  ambiguity  and  much  misunderstand- 


arisingfrom  j         j^   -^  reason  is  obvious,  because  we   usually   measure 

the  identity  7 

oftheordi-    masses  by  weighing,  and  most  often,  not  by  weighing  with  a 
nary  names    spring-balance,  but  bv  balancing  the  bodv  against  some  standard 

for  the  units  _      *  ,  , 

of  mass  and    mass,  which  standard  is  itself  affected  by  variations  of  gravity 
force.  in  the  same  proportion  as  the  body  weighed,  so  that  the  ratio  of 

their  masses  is  correctly  given  notwithstanding  such  variations. 
The  mass  of  a  given  body  —  the  number  of  "mass  units  "  in 
it  —  remains  invariable,  wherever  it  may  be  ;  its  weight,  on  the 
other  hand  —  the  number  of  "force  units"  which  measures  its 
tendency  to  fall,  as  judged  by  the  effort  required  to  lift  it,  or 
determined  by  a  spring-balance  —  depends  partly  on  where  it 
is.  At  the  equator  it  is  nearly  one  half  of  one  per  cent  less 
than  at  the  pole,  and  on  the  surface  of  the  moon  it  would  be 
only  about  one  sixth  as  great  as  on  the  earth. 

Professor  To  use  an  Illustration  suggested  by  Professor  Newcomb  :    Suppose  a 

Newcomb's     base-ball  team  could  somehow  get  to  the  moon.     They  would  find  their 

illustration.    bats  and  balls  very  light  to  lift  and  hold  ;  they  themselves  would  be  light 

on  their  feet  and  could  jump  six  times  as  high  and  as  far  as  on  the  earth, 

gravity  and  weight  being  so  much  less  than  here.     But,  since  masses  remain 


THE   EARTH   AS   AN  ASTRONOMICAL   BODY          125 

unchanged,  the  pitcher  could  not  with  a  given  exertion  send  the  ball  any 
more  swiftly  than  here,  nor  could  the  batter  hit  it  any  harder  or  give  it 
greater  speed  (though  it  would  fly  much  farther  before  it  fell),  and  the 
catcher  in  capturing  the  ball  would  receive  just  the  same  blow  upon  his 
hands  as  here.  And  if  they  had  a  steak  for  dinner  that  "  weighed  "  only 
two  pounds  on  their  spring-balance,  it  would  give  them  twelve  pounds 
of  meat ;  and,  we  may  add,  would  also  "  weigh "  twelve  pounds  on  a 
platform  scale,  or  steelyard. 

The  student  must  always  be  on  his  guard  whenever  he  comes 
to  the  word  "  pound  "  or  "  kilogram,"  or  any  of  their  congeners, 
and  must  consider  whether  he  is  dealing  with  units  of  mass  or 
of  force. 

142.  The  Scientific  Unit  of  Force  or  Stress,  —  the  Dyne,  Mega- 
dyne,  and  Poundal.  —  Many  high  authorities  now  urge  the  entire 
abandonment  of  the  old  force  units  which  bear  the  same  names 
as  the  mass  units,  and  the  substitution,  in  all  scientific  work  at 
least,  of  the  dyne  (Physics,  p.  33)  and  its  derivative,  the  mega- 
dyne.  The  change  would  certainly  conduce  to  clearness,  but 
for  a  time  at  least  would  be  inconvenient,  as  making  former 
mechanical  literature  almost  unintelligible  to  those  familiar 
with  the  new  units  only. 

The  Dyne  is  the  force  (pull  or  push)  which  acting  constantly  The  scien- 
for  one  second  upon  a  mass  of  one  gram  would  give  it  a  velocity  tific  unit  of 
of  one  centimeter  a  second.     It  equals  the  "  weight "  (at  Paris)  dyne. 

of  a  mass  of ^,  or  1.0199,  milligrams.     The  Megadyne  (a 

y  oUo 

million  dynes)  is  the  weight  (at  Paris)  of  a  mass  of  1.0199 
kilograms,  or  almost  exactly  1.02  kilograms  in  the  latitude  of 
Boston. 

Many  English  authorities,  however,  insist  on  a  unit  of  force 
based  on  the  British  units   of  mass   and  length  and  employ 
the  Poundal,  —  the  force  which  in  one  second  would  give  a  The  English 
velocity  of  one  foot  per  second  to  a  mass  of  one  pound.     Since  P°undal- 

1  9.805  meters  per  second  is  the  value  of  g  at  Paris. 


126 


MANUAL   OF   ASTRONOMY 


g  equals  (nearly)  32i-  feet  per  second,  the  poundal  is  about 

-— -  of   the  "  weight "   of  a  mass  pound  at  London,   or  very 
32J 

nearly  half  an  ounce  of  "  pull."     More  accurately,  the  poundal 
equals  13.865  dynes. 

143,  Gravitation.     The   Cause  of  Weight.  —  Science  cannot 
yet  explain  why  bodies  tend  to  fall  towards  the  earth  and  push  or 
pull  towards  it  when  held  from  moving ;  but  Newton  discovered 
and  proved  that  the  phenomenon  is  only  a  special  case  of  the 
much  more  general  fact  which  he  inferred  from  the  motions  of 
the  heavenly  bodies  and  formulated  as  the  Law  of  Gravitation, 
under  the  statement  that  any  two  -particles  of  matter  attract 
each  other  with  a  force  proportional  to  their  masses  and  inversely 
proportional  to  the  square  of  the  distance  between  them. 

If  instead  of  particles  we  have  bodies  composed  of  many 
particles,  then  the  total  force  between  the  bodies  is  the  sum  of 
the  attractions  of  all  the  different  particles,  each  particle  attract- 
ing every  particle  in  the  other  body  and  being  attracted  by  it. 

We  must  not  imagine  the  word  attract  to  mean  too  much.  It 
merely  states  as  a  fact  that  there  is  a  tendency  for  bodies  to  move 
towards  each  other,  without  including  or  implying  any  explana- 
tion of  the  fact.  Thus  far  none  has  appeared  which  is  less  diffi- 
cult to  comprehend  than  the  thing  itself.  It  remains  at  present 
simply  a  fundamental  fact,  though  it  is  not  impossible  (nor  im- 
probable) that  ultimately  it  may  be  shown  to  be  a  necessary  con- 
sequence of  the  relation  between  particles  of  ordinary  matter  and 
the  all-pervading  "ether"  to  which  we  refer  the  phenomena  of 
light,  radiant  heat,  electricity,  and  magnetism  (Physics,  p.  267). 

144,  The  Attraction  of  Spheres.  —  If  the  two  attracting  bodies 
are  spheres,  either  homogeneous  or  made  up  of  concentric  shells 
which  are  of  equal  density  and  thickness  throughout,  then,  as 
Newton  demonstrated,  the  action  on  bodies  outside  the  sphere 
is  precisely  the  same  as  if  all  the  matter  of  each  sphere  were 
collected  at  its  center.     If  the  distance  between  the  bodies  is  very 


THE   EARTH   AS   AN   ASTRONOMICAL   BODY          127 

great  compared  with  their  size,  then,  whatever  their  form,  the 
same  thing  is  nearly,  though  not  exactly,  true. 

He  also  showed  that  within  a  homogeneous  hollow  sphere  of  Attraction 
equal  density  and  thickness  throughout  the  attraction  is  every-  *e™  withm 
where  zero;  i.e.,  a  body  anywhere  within  the  hollow  shell  would  sphere, 
not  tend  to  fall  in  any  direction. 

If  bodies  which  attract  each  other  are  prevented  from  moving, 
the  effect  of  the  attraction  will  be  a  stress  (a  push  or  pull),  to  be 
measured  in  dynes  or  force  units  (not  in  mass  units),  and  this 
stress  is  given  by  the  equation  which  embodies  the  law  of  gravi-  Law  of 

tatioil,  Viz.,  gravitation 

M    X  M  expressed  as 

F  (dynes)  =  G  X  — *^g -•>  an  equation 

giving  the 

where  Ml  and  Jf2  are  the  masses  of  the  two  bodies  (expressed  *s  a  pull 
in  grams),  d  is  the  distance   between  their  centers   (in  centi-  in  dynes. 
meters],  and  G  is  a  factor  known  as  the  Newtonian  Constant  or 
the  Constant  of  Crravitation. 

145.   The  Constant  of  Gravitation.  —  The  constant  of  gravi-  The  con- 
tation  is  believed  to  be,  like  the  velocity  of  light,  an  absolute  stantof 

/.  ,T  -M    ,1  »  gravitation 

constant  of  nature,  —  the  same  in  all  the  universe  of  matter,  —  the  same 
among  the  stars  and  planets  as  well  as  upon  the  earth.    This  is  not  everywhere 
yet  absolutely  proved,  but  there  is  no  known  phenomenon  that  J^Jyerae. 
contradicts  it,  and  there  is  much  probable  evidence  in  its  favor. 
The  numerical  value  of  G  depends  on  the  units  of  mass, 
distance,  and  time ;    and   in   the    C.G.S.  system    (centimeter- 
gram-second)  it  is,  according  to  the   elaborate   determination 
of    Boys   in   1894,    0.00000006657    (6657  X  10"11)    or,   quite 
within   the   limits  of   experimental   error,  one  fifteen-millionth,  itsnumeri- 
If,  for  instance,  the  mass  M1  is  1000  grams,  M2  2000  grams,  cal  value 
and  the  distance  10  centimeters,  the  force  in  dynes  will  be  millionth 

in  the  C.G.S 
1  1000  X  2000      .  1  9nnn,  system  of 

15  000000          ~TOO~  '  15000000  ™its- 

or  y^  of  a  dyne. 


128  MANUAL   OF   ASTRONOMY 

It  may  be  added  that  it  is  not  yet  proved  that  the  equation  F  =  G  x  M± 
x  Jf2  -f-  r/2  is  the  complete  law.  It  is  conceivable  (though  highly  improb- 
able) that  the  right-hand  member  may  be  only  the  principal  term  of  a 
series  which  contains  other  terms  (involving  temperature,  for  instance) 
that  may  become  sensible  under  conditions  widely  different  from  any  yet 
observed.  And  "  matter  "  may  exist  which  does  not  "  gravitate  "  though 
possessing  "inertia,"  —  the  ether,  for  instance. 

146.  Acceleration  by  Gravitation.  —  If  Ml  and  M2  are  set  free 
while  under  each  other's  attraction,  they  will  at  once  begin  to 
approach  each  other.  At  the  end  of  the  first  second  M1  will 

M 

have  acquired  a  velocity  Vv  —  G  X  — |,  which,  the  student  will 

Cv 

observe,  depends  entirely  upon  the  mass  of  M2  and  not  at  all 
upon  that  of  Ml  itself.  (A  grain  of  sand  and  a  heavy  rock 
will  fall  at  the  same  rate  in  free  space  under  the  attraction  of  a 
given  body  when  at  the  same  distance  from  it.) 

Formula  Similarly,  M2  will  have   acquired  a  velocity  V2  =  G  X  — ^. 

giving  the  ** 

accelerating  The  speed  with  which  the  bodies  approach  each  other  will  be  the 
force  due  to  sum  o£  these  velocities,  and  if  we  denote  this  relative  accelera- 
in  centi-  tion  (or  the  velocity  of  approach  acquired  in  one  second)  by/", 

meters  per       we  snall  have 

second.  /. 


This  is  the  form  of  the  law  of  gravitation  which  is  used  in 
dealing  with  the  motions  of  the  heavenly  bodies,  caused  by  their 
attractions. 

Notice  that  while  the  expression  for  F  (the  stress  in  dynes) 
has  the  product  of  the  masses  in  its  numerator,  that  for  /  (the 
relative  acceleration)  has  their  sum,  and,  like  g,  is  expressed  in 
centimeters  per  second. 

147.  We  are  now  prepared  to  discuss  the  methods  of  meas- 
uring the  earth's  mass.  It  is  only  necessary  to  compare  the 
attraction  which  the  earth  exerts  on  a  body,  m,  on  its  surface 
(at  a  distance,  therefore,  of  3959  miles  from  its  center)  with  the 


THE   EARTH   AS   AN   ASTRONOMICAL   BODY          129 

attraction  exerted  upon  m  by  some  other  body  of  a  known  mass  Mass  of 

at  a  known  distance.     The  practical  difficulty  is  that  the  attrac-  earth  meas~ 

,  ,      ,      ,       .  ,  uredbycom- 

tion  of  any  manageable  body  is  so  extremely  small,  compared  paring  its 

with   the    attraction  of   the   earth,   that   the    experiments   are  attraction 

exceedingly  delicate.     Unless  the  mass  employed  for  compari-  at  its  sur_ 

son  with  the  earth  is  one  of  several  tons,  its  attraction  will  be  *ace  with 

only  a  fraction  of  a  dyne,  —  hard  to  detect  even,  and  worse  to  known 

measure.  attracting 


The  various  experimental  methods  which  have  been  actually 
used  thus  far  for  determining  the  earth's  mass  are  enumerated  known 
and  discussed  in  the  author's  General  Astronomy,  to  which  the  dlstance- 
student  is  referred.     We  present  here  only  a  single  one,  which 
is  not  difficult  to  understand  and  is  probably  the  best,  though 
not  quite  the  earliest. 

148.  The  Earth's  Mass  and  Density  determined  by  the  Torsion  The  torsion 
Balance.  —  This  is  an  apparatus  invented  by  Michell  and  first  balance- 
employed  by  Lord  Cavendish  in  1798.  A  light  rod  carrying 
two  small  balls  at  its  extremities  is  suspended  at  its  center  by 
a  fine  wire,  so  that  -the  rod  will  hang  horizontally.  If  it  be 
allowed  to  come  to  rest,  and  then  a  very  slight  deflecting  force 
be  applied,  the  rod  will  be  drawn  out  of  position  by  an  amount 
depending  on  the  stiffness  and  length  of  the  wire  as  well  as  the 
intensity  of  the  force.  When  the  deflecting  force  is  removed 
the  rod  will  vibrate  back  and  forth  until  brought  to  rest  by  the 
resistance  of  the  air. 

The   Coefficient  of  Torsion,  as  it  is  called,  —  i.e.,  the  stress  Determina- 
which  will  produce  a  twist  of  one  revolution,  —  can  be  accu-  tion  of  the 

coefficient 

rately  determined  by  observing  the  time  of  free  vibration  when  Of  torsion 
the  dimensions  and  masses  of  the  rod  and  balls  are  known  (see  bj  observa- 
Anthony  and  Brackett,  Physics,  p.  117),  and  this  coefficient  will 
enable  us  to  determine  what  force  in  dynes  is  necessary  to  pro- 
duce a  twist  or  deflection  of  any  number  of  degrees.     If  the 
wire  is  stiff  the  coefficient  will  be  large,  and  correspondingly 
small  if  very  slender.     It  is  therefore  desirable  that  it  should 


130 


MANUAL   OF   ASTRONOMY 


of  deflection 
caused  by 
attraction. 


be  as  slender  as  possible,  while  yet  sufficiently  strong  to  sustain 
the  rod  and  balls. 

149.   The  Observations. —  If,  now,  after  the  torsional  coeffi- 
cient has  been  carefully  determined  by  observing  the  free  vibra- 
Observation   tions  of  the  rod,  two  large  balls,  A  and  B  (Fig.  50),  are  brought 
near  ^  smaller  ones,  a  deflection  will  be  produced  by  their 
attraction,  and  the  small  balls  will  move  from  a  and  b  (their 

position  of  rest)  to  a'  and  V.  By 
shifting  the  large  balls  to  the  other 
side  at  A'  and  B'  (which  can  be 
done  by  turning  the  frame  upon 
which  they  are  supported)  we  shall 
get  a  similar  deflection  in  the  oppo- 
site direction,  —  i.e.,  from  a1  and  bf 
to  a"  and  b",  —  and  the  difference 
between  the  two  positions  assumed 
by  the  two  small  balls  —  i.e.,  the 
distance  a'a"  and  b'b"  —  will  be 
twice  the  deflection  which  is  due 
to  the  attraction  of  the  two  large 
lolls  for  the  two  small  balls. 

The  observations  of  vibration 
and  deflection  are  best  made  by 
watching  with  a  telescope  from  a 

distance  the  reflection  of  a  fixed  scale  in  a  little  mirror  attached 
to  the  horizontal  beam  at  C. 

In  observing  the  deflections  it  is  not  necessary,  nor  even  best, 
to  wait  for  the  balls  to  come  to  rest.  While  still  vibrating 
we  note  the  extremities  of  their  swing.  The  middle  point  of 
the  swing  (with  a  slight  correction)  gives  the  place  of  equilib- 
rium. We  must  also  carefully  determine  the  distances  Aa\ 
A'b",  Bb',  and  B'a"  between  the  center  of  each  of  the  large  balls 
and  the  center  of  the  small  ball  when  deflected.  The  utmost 
care  must  be  taken  to  exclude  air  currents  and  electrical  or 


FIG.  50.  —  Plan  of  the  Torsion 
Balance 


THE   EARTH   AS   AN   ASTRONOMICAL   BODY          131 

magnetic  disturbances,  since  these  would  seriously  vitiate  the 
results. 

150.   Calculation  of  the  Earth's  Mass  from  the  Experiment.  — 
The  earth's  attraction  on  each  of  the  small  balls,  m,  is  evidently 
measured  by  the  ball's  weight,  w,  corrected  for  the  centrifugal 
force    of   the    earth's  rotation    at   the    observer's    station    and 
reduced  to  dynes. 

The  attractive  force  of  the  large  ball  on  the  small  one  near  it  Calculation 
is  found  from  the  observed  deflection.      If,  for  instance,  this  ofearth's 

mass. 

deflection  is  one  degree,  and  the  coefficient  of  torsion  is  such 
that  it  takes  a  force  of  ten  dynes  at  the  end  of  the  rod  to  twist 
the  wire  one  whole  turn,  then  the  deflecting  force,  which  we 
will  call  2/,  will  be  ^  of  a  dyne.  One  half  of  this  deflecting 
force,  /,  will  be  due  to  A9  8  attraction  of  a,  and  half  to  .Z?'s 
attraction  of  I.  Call  the  mass  of  the  large  ball  B,  determined 
by  its  weight,  and  that  of  the  small  ball  m,  and  let  d  be  the 
measured  distance  Bbf  between  their  centers.  We  shall  then 
have,  from  Sec.  144,  the  equation 


Similarly,  calling  E  the  mass  of  the  earth  and  R  its  radius,  w 
being  the  corrected  weight  in  dynes  of  the  small  ball,  we  shall 

have 


Dividing  equation  (a)  by  (5),  G  and  m  cancel  out,  and  we  have 

E      fw\  /R2\ 

-  =  [-)(  —  ),  or  J£  =  . 

which  gives  the  mass  of  the  earth  in  terms  of  B. 

By  the  same  observations  the  value  of  the  constant  of  gram-  Determina- 

-P .  ^2  tionof  eon- 

tation  is  determined,  since,  from  equation  (a),  G  = -,  B  and  stantof 

•*» '  m  gravitation. 

m  being  both  measured  in  grams*  and  d  in  centimeters. 


132 


MANUAL   OF   ASTRONOMY 


Direct 
determina- 
tion of 


previous 
calculation 
of  its  mass. 


151.  Density  of  the  Earth.  —  Having  the  mass  of  the  earth 
it  is  easy  to  find  its  density.     The  volume,  or  bulk,  in  cubic 
miles  has  already  been  given  (Sec.  139)  and  can  be  reduced  to 
cubic  feet  by  simply  multiplying  that  number  by  the  cube  of 
5280.     Since  a  cubic  foot  of  water  contains  62|  mass  pounds 
(nearly),  the  mass  which  the  earth  would  have,  if  composed  of 
water,  follows.     Comparing  this  with  its  mass  obtained  from  the 
observations,  we  get  its  density. 

A  combination  of  the  results  of  all  the  different  methods 
hitherto  employed,  taking  into  account  their  relative  accuracy, 
gives  about  5.53  as  the  most  probable  value  of  the  earth's 
density  compared  with  water,  but  the  second  decimal  is  not 
secure. 

152.  Density  determined  directly. — We  can  deduce  the  earth's  density 
directly  from  the  observations  without  any  preliminary  calculation  of  its 
mass. 

Letting  r  and  s  represent  the  radius  and  density  of  the  ball  B,  its  mass 
is  f7rrss.  Similarly,  E,  the  mass  of  the  earth,  is  fTrfilV,  s'  being  the 
earth's  mean  density. 

Substituting  these  values  of  B  and  E  in  equations  (a)  and  (6)  of  the 
preceding  section,  we  have 


and 


wR* 

Gm 


(d) 


Rss'      wR2 
Dividing  (d)  by  (c),  we  get     —  =  — , 

T  S  J 

whence,  finally,  s'  =  s  x  - 


and 


giving  the  density  of  the  earth  in  terms  of  the  density  of  the  ball 
other  known  quantities. 

Early  experi-        153.    In  the  earlier  experiments,  by  this  torsion-balance  method,  the 

ments.  small  balls  were  of  lead  1  or  2  inches  in  diameter,  at  the  extremities  of 

a  light  wooden  rod  5  or  6  feet  long  inclosed  in  a  case  with  glass  ends,  and 

their  positions  and  vibrations  were  observed  by  a  telescope  looking  directly 

at  them  from  a  distance  of  several  feet.     The  attracting  masses,  A  and  Bt 


THE   EARTH    AS   AN   ASTRONOMICAL   BODY          133 

were  balls  (also  of  lead)  about  a  foot  in  diameter.     Great  difficulties  were 
encountered  from  currents  of  air  within  the  inclosure. 

Boys  in  1894  used  a  most  refined  apparatus  in  which  the  small  balls  (of   Experi- 
gold),  one  quarter  of  an  inch  in  diameter,  were  hung  at  the  end  of  a  beam  ments  of 
only  a  centimeter  long,  which  was  suspended  by  a  delicate  fiber  of  amor-     ro  esi 
phous  quartz,  an  ingenious  invention  of  the  experimenter.     The  deflections 
due  to  the  attraction  of  two  sets  of  lead  balls,  respectively  2£  and  4±  inches 
in  diameter,  were  measured  by  observing  with  a  telescope  the  reflection  oi 
a  scale  in  a  little  mirror  attached  to  the  beam.     The  whole  apparatus  was 
placed  in  an  air-tight  case  no  larger  than  an  ordinary  water  pail,  from 
which  the  air  was  exhausted  and  a  little  hydrogen  admitted  to  take  its 
place.     His  result  for  the  earth's  density  was  5.527.     It  was  from  these 
experiments  that  the  value  of  the  constant  of  gravitation  already  given  was 
deduced. 

Different  values  for  the  earth's  density,  obtained  by  experiments  during 
the  last  fifty  years,  range  all  the  way  from  5.8  to  4.9,  omitting  one  or  two 
which  are  very  discordant  from  circumstances  easily  understood. 

154.  Constitution  of  the  Earth's  Interior.  —  Since  the  average 
density  of  the  earth's  crust  does  not  exceed  three  times  that  of 
water,  while  the  mean  density  of  the  whole  earth  is  about  5.5,  increase 
it  is  obvious  that  at  the  earth's  center  the  density  must  be  very  °^^ty 
much  greater  than  at  the  surface,  —  very  likely  as  high  as  eight  earth's 
or  ten  times  the  density  of  water,  and  perhaps  higher,  —  equal  center- 
to  that  of  the  heavier  metals.     There  is  nothing  surprising  in 
this.     If  the  earth  were   ever  fluid,  it  is  natural  to  suppose 
that  before  solidification  took  place  the  densest  materials  would 
settle  towards  the  center. 

Whether  the  interior  of  the  earth  is  solid  or  fluid,  it  is  diffi- 
cult to  say  with  certainty.     Certain  tidal  phenomena,  to  be 
mentioned   hereafter,   have  led    Lord    Kelvin   to  express    the 
opinion  that  "  the  earth  as  a  whole  is  solid  throughout,  and  Question 
about  as  rigid  as  steel,"  volcanic  centers  being  mere  "pustules,"  astothe 

rigidity  or 


so  to  speak,  in  the  general  mass.      To  this   most  geologists  plasticity  oi 
demur,  maintaining  that  at  a  depth  of  not  many  hundred  miles  the  central 
the  materials  of  the  earth  must  be  fluid  or  at  least  semi-fluid. 
This  is  inferred  from  the  phenomena  of  volcanoes  and  from  the 


134  MANUAL   OF   ASTRONOMY 

fact  that  the  temperature  continually  increases  with  the  depth 
so  far  as  we  have  yet  been  able  to  penetrate.  But  thus  far  the 
deepest  penetration  is  but  little  more  than  a  single  mile,  —  a 
mere  scratch,  —  not  -g^Vo  part  of  the  distance  to  the  center  of 
the  earth. 

EXERCISES 

1.  Does   the  transportation  of   sediment  by  the   Mississippi  tend  to 
lengthen  or  to  shorten  the  day? 

2.  If   the   diameter   of    the    earth   were    doubled,    keeping    its    mass 
unchanged,  how  would  its  density  and  the  weight  of  bodies  at  its  surface 
be  affected? 

3.  If  its  diameter  were  trebled,  keeping  its  density  unchanged,  how 
much  would  its  mass  and  the  weight  of  bodies  at  its  surface  be  increased? 

4.  Supposing  the  earth  to  be  homogeneous,  how  great  (approximately) 
would  be  the  force  of  gravity  1000  miles  below  its  surface? 

Solution.  Inside  of  a  hollow  sphere  the  attraction  is  zero  (Sec.  144).  At 
the  depth  of  1000  miles,  therefore,  the  effective  attraction  would  be  that 
of  a  sphere  of  only  3000  miles  radius,  all  the  shell  of  matter  outside  of  this 
being  without  influence.  We  should  therefore  have  gravity  at  the  surface : 

gravity  1000  miles  below  the  surface  =  f  —  :  f  7r(fi-1000)8  =  E:(R-  1000) ; 

J?2         (It  —  1000)2 

i.e.,  as  4000  : 3000.  In  words,  the  attraction  at  this  depth  would  be  £  that  at 
the  surface  of  the  earth,  if  it  were  of  equal  density  throughout,  which  it  is  not. 

5.  Assuming  g  at  the  earth's  surface  to  be  9.805  meters  per  second, 
what  would  it  be  in  a  balloon  at  an  elevation  of  2  miles  ?     The  radius  of 
the  earth  may  be  taken  as  4000  miles  and  centrifugal  force  neglected. 

Ans.    9.7952  m  per  second. 

Would  the  value  of  g  be  the  same  at  the  top  of  a  mountain  2  miles 
high,  and  if  not,  why  ? 

6.  Given  two  spheres  one  of  which  has  a  mass  m  times  greater  than  the 
other ;  on  what  point  on  the  line  joining  their  centers  are  their  attractions 
equal  ? 

Solution.  Let  d  be  the  distance  between  their  centers  and  x  the  distance 
of  the  point  of  equilibrium  from  the  smaller  body ;  then  the  attraction  of  the 

larger  body  at  that  point  is  G — — — ,  that  of  the  smaller  being  G  — .     Cancel- 

(a  —  x)2  r—  y? 

ing  the  (?'s  and  taking  the  square  roots,  we  have ^—  =  - »  from  which  we 

have  (<*-*)      * 

A                     d 
Ans.   x  = — . 

1  +  Vm 


THE   EARTH   AS   AN   ASTRONOMICAL   BODY 


135 


7.  Assuming  the  moon's  mass  as  ^T  of  the  earth's,  where  is  the  equi- 
librium point  on  the  line  of  centers  ? 

Ans.    At  a  point  -£$  of  the  distance  from  the  moon  to  the  earth. 

8.  What  is  the  attraction  in  dynes  between  two  spheres,  each  having  a 
mass  of  1000  kilograms,  at  a  distance  of  1  meter  between  centers  ? 

Ans.    6f  dynes,  or  the  weight  of  6.8  mgm. 

9.  If  these  spheres  were  free  to  move  under  their  mutual  attraction, 
required  their  relative  velocity  at  the  end  of  one  second. 

Ans.    y^o^  mm  per  second. 

10.  If  at  a  distance  of  half  a  meter  from  such  a  ball  is  suspended  a 
small  ball  weighing  1  gram,  what  is  the  attraction  between  them  ? 

Ans.    •375^0'  °f  a  dyne. 

11.  If   in  this  case  the  small  ball  were   suspended    by  a  fine  thread 
10  meters  long,  how  many  millimeters  would  it  be  drawn  from  a  vertical 
position,  and  what  angle  would  the  thread  make  with  the  vertical? 

Deviation,  0.000272  mm. 


Ans. 


Deflection,  0".00561. 


Yerkes  Observatory 


CHAPTER  VI 


Sun's  appar- 
ent motion 
in  declina- 
tion. 


Its  motion 
in  right 
ascension. 


THE  ORBITAL  MOTION  OF  THE  EARTH 

The  Apparent  Motion  of  the  Sun,  and  the  Orbital  Motion  of  the  Earth  —  Precession 
and  Nutation  —  Aberration  —  The  Equation  of  Time  —  The  Seasons  and  the 
Calendar 

155.   The  Sun's  Apparent  Annual  Motion  among  the  Stars.  - 

This  must  have  been  among  the  earliest  recognized  of  astronom- 
ical phenomena,  as  it  is  obviously  one  of  the  most  important. 

As  seen  by  us  in  the  northern  hemisphere,  the  sun,  starting 
in  the  spring  at  the  vernal  equinox,  mounts  higher  in  the  sky 
each  day  at  noon  for  three  months,  until  the  summer  solstice, 
and  then  descends  towards  the  south,  reaching  in  the  autumn 
the  same  noonday  elevation  which  it  had  in  the  spring.  It 
keeps  on  its  southward  course  to  the  winter  solstice  in  Decem- 
ber and  then  returns  to  its  original  height  at  the  end  of  a  year, 
marking  and  causing  the  seasons  by  its  course. 

Nor  is  this  all.  The  sun's  motion  is  not  merely  north  and 
south,  but  it  also  advances  continually  eastward  among  the 
stars.  In  the  spring  the  stars  which  at  sunset  are  rising  on  the 
eastern  horizon  are  different  from  those  which  are  found  there 
in  summer  or  winter. 

In  March  the  most  conspicuous  of  the  eastern  constellations  at  sunset 
are  Leo  and  Bootes.  A  little  later  Virgo  appears,  in  the  summer  Ophiu- 
chus  and  Libra ;  still  later  Scorpio,  while  in  midwinter  Orion  and  Taurus 
are  ascending  as  the  sun  goes  down. 

So  far  as  the  obvious  appearances  are  concerned,  it  is  quite 
indifferent  whether  we  suppose  the  earth  to  revolve  around  the 
sun  or  vice  versa.  That  the  earth  is  the  body  which  really 
moves,  however,  is  absolutely  demonstrated  by  three  phenomena 

136 


THE  ORBITAL  MOTION  OF  THE  EARTH      1ST 

too  delicate  for  observation  without  the  telescope,  but  accessible  Facts  which 
to  modern  methods.     The   most  conspicuous   of  them  is  the  ^emonstrate 

tllJit  tll6 

aberration  of  light ;  the  others  are  the  regular  annual  shift  of  apparent 
the  lines  in  the  spectra  of  stars  and   the  annual  parallax  of  motlouof 

the  sun  is 

the  stars.  due  to  the 

156,   The  Ecliptic ;  its  Related  Points  and  Circles.  — By  observ-  real  motion 
ing  daily  with  the  meridian-circle  both  the  sun's  declination 
and  also  the  difference  between  its  right  ascension  and  that  of 
some  chosen  star,  we  obtain  a  series  of  positions  of  the  sun's 
center  which  can  be  plotted  on  a  globe,  and  we  can  thus  mark 
out  its  path  among  the  stars.     It  is  a  great  circle,  called  the 
Ecliptic   (Sec.   23),   which  cuts  the  equator   at   two    opposite  The  ecliptic 
points  (equinoxes),  at  an  angle  of  approximately  23£°  (23°  27'  defined' 
8".0  in  1900).     It  gets  its  name  from  the  fact,  early  discovered, 
that  eclipses  happen  only  when  the  moon  is  crossing  it.     It  is 
the  great  circle  in  which  the  plane  of  the  earths  orbit  cuts  the 
celestial  sphere. 

The  angle  which  the  ecliptic  makes  with  the  equator  at  the 
equinoctial  points  is  called  the  Obliquity  of  the  Ecliptic  and  is  Obliquity  of 
evidently  equal  to  the  sun's  maximum  declination,  reached  in  the  ecllPtlc- 
June  and  December. 

The  two  points  in  the  ecliptic  midway  between  the  equinoxes 
are    called   the    Solstices,    because    there    the    sun    apparently  Solstices 
"stands,"   i.e.,  stops    and   reverses  its   motion   in  declination.  andtr°Plcs- 
The    circles    drawn    through   these    solstices    parallel    to    the 
equator  are  called  the   Tropics. 

The  Poles  of  the  Ecliptic  are  the  two  points  in  the  heavens  The  poles  of 
90°  distant  from  every  point  in  that  circle.     The  northern  one  the  ecliPtic- 
is  in  the  constellation  Draco,  about  midway  between  the  stars 
8  and  f,  and  on  the  solstitial  colure  (right  ascension,  18  hours), 
its  distance  from  the  pole  of  rotation  being  equal  to  the  obliquity 
of  the  ecliptic  (see  Sec.  27). 

It  will  be  remembered  that  celestial  latitude  and  longitude  are 
measured  with  reference  to  the  ecliptic  and  not  to  the  equator. 


138 


MANUAL   OF   ASTRONOMY 


157.  The  Zodiac  and  its  Signs.  —  A  belt  16°  wide  (8°  on  each 
The  zodiac,  side  of  the  ecliptic)  is  called  the  zodiac,  or  "  zone  of  animals  " 
(German,  Thierkreis),  the  constellations  in  it,  excepting  Libra, 
being  all  figures  of  living  creatures.  It  is  taken  of  that  par- 
ticular width  simply  because  the  moon  and  the  principal  planets 
always  keep  within  it.  It  is  divided  into  the  so-called  "  signs," 
each  30°  in  length,  having  the  following  names  and  symbols  : 


Signs  01  the 
zodiac. 


Aries     °f 

Spring    -  Taurus  $ 

Gemini  n 

(  Cancer  °5 

Summer  •{  Leo        $, 


Virgo 


f  Libra  ±± 

Scorpio          TI\ 
L  Sagittarius    $ 
( Capricornus  VJ 
Winter    J  Aquarius      zx 
Pisces  X 


Distinction 
between  the 
ecliptic  and 
the  orbit  of 
the  earth. 


Observa- 
tions for 
determining 
the  form  of 
the  orbit. 


The  symbols  are  for  the  most  part  conventional  pictures  of  the  objects. 
The  symbol  for  Aquarius  is  the  Egyptian  character  for  water.  The  origin 
of  the  signs  for  Leo,  Capricornus,  and  Virgo  is  not  quite  clear. 

The  zodiac  is  of  extreme  antiquity.  In  the  zodiacs  of  the 
earliest  history  the  Lion,  Bull,  Ram,  and  Scorpion  appear 
precisely  as  now. 

158.  The  earth's  orbit  is  the  path  in  space  pursued  by  the 
earth  in  its  revolution  around  the  sun.  The  ecliptic  is  not  the 
orbit  and  must  not  be  confounded  with  it ;  it  is  simply  a  great 
circle  of  the  infinite  celestial  sphere,  while  the  orbit  itself  is 
(nearly)  a  circle,  of  finite  diameter,  in  space.  The  fact  that  the 
ecliptic  is  a  great  circle  gives  us  no  information  about  the  orbit, 
except  that  it  lies  wholly  in  one  plane,  which  passes  through  the 
sun;  it  tells  us  nothing  as  to  the  orbit's  real/orm  or  size. 

By  reducing  the  daily  observations  of  the  sun's  right  ascen- 
sion and  declination  made  with  a  meridian-circle  to  celestial 
longitude  and  latitude  (the  latitude  would  always  be  exactly 
zero,  except  for  some  slight  perturbations  of  the  earth)  and 
combining  these  data  with  observations  of  the  sun's  apparent 
diameter,  we  can,  however,  ascertain  the  form  of  the  earth's 


THE  ORBITAL  MOTION  OF  THE  EARTH 


139 


orbit  and  the  law  of  its  motion  in  this  orbit.  The  size  of  the 
orbit  cannot  be  fixed  until  we  find  some  means  of  determining 
the  scale  of  miles. 

159.   To  find  the  Form  of  the  Orbit Take  a  point,  S  (Fig.  51), 

for  the  sun,  and  draw  through  it  a  line,  OS°f ,  directed  towards  the 

vernal  equinox,  from  which   longitudes    are  measured.     Lay  Direction  of 

off  from  S  lines  indefinite  in  length,  making  angles  with  S  <¥>  earth  from 

'     sun  on  days 

equal  to  the  earth  s  longitude  as  seen  from  the  sun  -1  on  each  of  Of  observa- 
the  days  when  observations  were  made.     We  shall  thus  get  a  tion> 
sort  of    "spider,"    showing 
the  direction  of  the  earth  as 
seen  from  the  sun  on  each 
of  those  days. 

Next,  as  to  the  distances. 
While  the  apparent  diameter 
of  the  sun  does  not  deter- 
mine its  absolute  distance 
from  the  earth  unless  we 
know  the  diameter  in  miles, 
yet  the  changes  in  the  appar- 
ent diameter  do  inform  us 
as  to  the  relative  distance 
at  different  times,  —  the  distance  being  inversely  proportional  Relative 
to  the  sun's  apparent  diameter  (Sec.  10).  If,  then,  on  this  fstance 

from  sun  on 

"spider"  we  layoff  distances  equal  to  the  quotient  obtained  these  days, 
by  dividing  some  constant,  say  10000,  by  the  sun's  apparent 
diameter  in  seconds  as  observed  at  each  date,  these  distances 
will  be  proportional  to  the  true  distance  of  the  sun  from  the 
earth,  and  the  curve  joining  the  points  thus  obtained  will  be  a 
true  map  of  the  earth's  orbit,  though  without  any  scale  of  miles. 
When  the  operation  is  performed,  we  find  that  the  orbit  is 
an  ellipse  of  small  eccentricity  (about  ^),  with  the  sun  not  in 
the  center,  but  at  one  of  the  two  foci. 

1  This  is  18Q9  +  the  sun's  longitude  as  seen  from  the  earth. 


FIG.  51.  —  Determination  of  the  Form  of  the 
Earth's  Orbit 


140 


MANUAL   OF   ASTRONOMY 


Definition  of 
the  ellipse, 
its  axes,  and 
eccentricity. 


Definition  of 

perihelion, 

aphelion, 

radius 

vector,  and 

anomaly. 


Discovery 
of  the  eccen- 
tricity of 
the  earth's 
orbit  by 
Hipparchus. 


160.  Definitions  relating  to  the  Orbital  Ellipse The  Ellipse 

is  a  curve  such  that  the  sum  of  the  two  distances  from  any  point  on 
its  circumference  to  two  points  within,  called  the  foci,  is  always 
constant  and  equal  to  the  major  axis  of  the  ellipse. 

In  Fig.  52,  wherever  P  is  taken  on  the  periphery  of  the 
ellipse,  SP  +  PF  always  equals  AA',  which  is  the  major  axis. 
AC  is  the  semi-major  Axis  and  is  usually  denoted  by  A  or  a. 
BC  is  the  semi-minor  Axis,  denoted  by  I?  or  b ;  the  eccentricity 

&ri 

of   the    ellipse    is    the  fraction,   or  ratio,  — ,  and  is   usually 


expressed  as  a  decimal.     It  equals 


FIG.  52.  — The  Ellipse 


If  a  cone  is  cut  across  obliquely  by  a  plane,  the  section  is  an 

ellipse,  which  is  therefore  called 
one  of  the  conic  sections.  (See 
Sec.  314.) 

Perihelion  and  Aphelion  are 
respectively  the  points  where 
the  earth  is  nearest  to  and 
remotest  from  the  sun,  the  line 
joining  them  being  the  major 
axis  of  the  orbit.  The  Line  of 
Apsides  is  the  major  axis  indefi- 
nitely produced  in  both  directions.  A  line  drawn  from  the 
sun  to  the  earth  or  any  other  planet  at  any  point  in  its 
orbit,  as  SP  in  the  figure,  is  called  the  planet's  Radius  Vector, 
and  the  angle  ASP,  reckoned  from  the  perihelion  point,  in 
the  direction  of  the  planet's  motion  towards  B,  is  called  its 
Anomaly. 

161.  Discovery  of  the  Eccentricity  of  the  Earth's  Orbit  by 
Hipparchus.  —  The  variations  in  the  sun's  diameter  are  too 
small  to  be  detected  without  a  telescope,  so  that  the  ancients 
failed  to  perceive  them.  Hipparchus,  however,  about  120  B.C., 
discovered  that  the  earth  is  not  in  the  center  of  the  circular 


THE   ORBITAL   MOTION   OF   THE   EARTH  141 

orbit,1  which  he  supposed  the  sun  to  describe  around  it  with 
uniform  velocity. 

Obviously,  the  sun's  apparent  motion  is  not  uniform,  because 
it  takes  186  days  for  the  sun  to  pass  from  the  vernal  equinox 
to  the  autumnal,  and  only  179  days  to  return.  Hipparchus 
explained  this  difference  by  the  hypothesis  that  the  earth  is  out 
of  the  center  of  the  circle. 

In  fact,  the  earth's  orbit  is  so  nearly  circular  that  the  differ- 
ence between  the  radius  vector  of  the  ellipse  and  that  of  the 
eccentric  circle  of  Hipparchus  is  everywhere  so  small  that  the 
method  indicated  in  the  preceding  article  would  not  practically 
suffice  to  discriminate  between  them.     Other  planetary  orbits 
are,  however,  unmistakable  ellipses, 
and  the  investigations  of  Newton 
show  that  the  earth's  orbit  also  is 
necessarily  elliptical. 

162.  The  Law  of  the  Earth's 
Motion.  —  By  comparing  the  meas- 
ured apparent  diameter  of  the  sun 
with  the  differences  of  longitude 
from  day  to  day,  we  can  deduce  FIG.  53.— Equable  Description 
not  only  the  form  of  the  orbit,  but  of  Areas 

the  law  of  the  earth's  motion  in  it.     On  arranging  the  daily 
motions    and    apparent    diameters    in    a   table,    we    find   that 
the  daily  motions  vary  directly  as  the  squares  of  the  diame-  The  law  of 
ters,  or  inversely  as  the  squares  of  the  distances  of  the  earth  theeartn's 
from  the  sun.     In  other  words,  the  product  of  the  square  of  motion  — 
the  distance  by   the   daily   motion    is    constant.     Now    the    area  thelawof 
of  any  small  elliptical  sector  cSd  (Fig.  53)  which  is  sensibly  in  equal 
a  triangle  =  1  Sc  •  Sd   sin  cSd,  or  1  r'r"  sin  cSd.     When  the   times- 

1  Until  the  time  of  Kepler,  it  was  universally  assumed  on  metaphysical 
grounds  that  the  orbits  of  the  celestial  bodies  must  necessarily  be  circular  and 
described  with  a  uniform  motion,  "because,"  as  was  reasoned,  "the  circle  is 
the  only  perfect  curve,  and  uniform  motion  is  the  only  perfect  motion  proper  to 
heavenly  bodies." 


142 


MANUAL   OF   ASTRONOMY 


Demonstra- 
tion of  the 
law  of  areas 
from  obser- 
vation. 


Kepler's 
Problem. 


angle  is  small  r1  X  r"  =  (sensibly)  r2,  r  being  the  "  radius  vector  " 
drawn  to  the  middle  of  cd ;  and  for  sin  cSd  we  may  put  cSd 
itself.  Hence,  area  cSd  =  ^  r2  x  cSd,  —  a  constant,  as  obser- 
vation shows;  or,  in  other  words,  its  radius  vector  describes 
areas  proportional  to  the  times,  a  law  which  Kepler  first  discov- 
ered in  1609. 

If  in  Fig.  53  ab,  cd,  and  ef  be  portions  of  the  orbit  described 
by  the  earth  in  different  weeks,  the  areas  of  the  elliptical  sectors 
aSb,  cSd,  and  eSf  are  all  equal.  A  planet  near  perihelion 
moves  faster  than  at  aphelion  in  just  such  proportion  as  to  pre- 
serve this  relation. 

163.  As  Kepler  left  the  matter  this  is  a  mere  fact  of  obser- 
vation. He  could  give  no  reason  for  it.  Newton  afterwards 

proved  that  it  is  a  necessary  con- 
sequence of  the  fact  that  the  earth 
moves  under  the  action  of  a  force 
always  directed  towards  the  sun 
(Sees.  303  and  304).  The  law 
holds  good  in  every  case  of  orbital 
motion  under  a  central  attraction 
and  enables  us  to  find  the  position 
of  the  earth  or  any  planet,  at  any 
time,  when  we  once  know  the  time  of  its  orbital  revolution,  or 
"period,"  and  a  date  when  it  was  at  perihelion.  Thus,  the  angle 
ASP  (Fig.  54),  or  the  anomaly  of  the  planet,  must  be  such  that  the 
shaded  area  of  the  elliptical  sector  ASP  will  be  that  portion  of 

the  whole  ellipse  which  is  represented  by  the  fraction  — ,  T  being 

the  number  of  days  in  the  period  and  t  the  number  of  days 
since  the  planet  last  passed  perihelion.  The  solution  of  this 
problem,  known  as  Kepler's  Problem,  leads  to  a  "transcen- 
dental" equation,  and  can  be  found  in  all  books  on  phys- 
ical astronomy,  or  in  the  Appendix  to  the  author's  G-eneral 
Astronomy. 


FIG.  54.  — Kepler's  Problem 


THE  ORBITAL  MOTION  OF  THE  EARTH     143 

164,   Changes  in  the  Orbit  of  the  Earth.  —  Were  it  not  for  the 

attraction  of  the  planets  upon  the  earth  and  sun,  the  earth  would  Effect  of 
maintain -her  orbit  strictly  unaltered  from  age  to  age,  except  ^^^s 
that  possibly  in  the  course  of  millions  of  years  the  effect  of  upon  the 
falling  meteors  and  the  attraction  of  some  of  the  nearer  stars  earth's 

motion. 

might  become  barely  sensible.      In  consequence,  however,  01 

the  attractions  of  the  other  planets,  it  is  found  that,  while  the  Major  axis 

Major  Axis  of  the  orbit  and  the  Length  of  the  Year  remain  in  and  j?erioc? 

unaffected 

the  long  run  unchanged,  other  elements  undergo  slow  variations  in  the 
known  as  "  secular  perturbations."  long  run- 

(1)  Revolution  of  the  Line  of  Apsides.     This  line,  which  now 
stretches  in  both  directions  towards  the  opposite  constellations 

of  Gemini  and  Sagittarius,  moves  continually  eastward  (i.e.,  in  Eastward 
the  same  direction  as  the  planetary  motions)  at  a  rate  which  j^™1^™ 
would  carry   it   completely    around    the    circle    in   about   one  Of  apsides, 
hundred    and    eight    thousand   years,    if    the    rate    continued 
always  the  same  as  at  present,  —  which,  however,  it  will  not, 
since  it  is  affected  by  changes  in  the  eccentricity  and  by  other 
circumstances. 

(2)  Change  of  Eccentricity.     At  present  the  eccentricity  of  Change  of 
the  earth's  orbit,  now  0.016,  is  slowly  diminishing,  and  accord-  eccentricity 

—  at  present 

ing  to  Leverrier  will  continue  to  do  so  for  about  twenty-four  siowiy 
thousand  years,  when  it  will  be  only  0.003 ;  i.e.,  the  orbit  will  diminishing, 
become  almost  circular.     Then  it  will  increase  again  for  some 
forty  thousand  years  and  will  continue  to  oscillate,  always  keep- 
ing between  zero  and  0.07.     But  the  successive  oscillations  are 
not  equal  either  in  amount  or  time,  —  not  at  all  like  the  "  swing 
of  a  mighty  pendulum,"  which  has  been  rather  a  favorite  figure 
of  speech  with  some  writers. 

(3)  Change  in  the    Obliquity  of  the  Ecliptic.     The  plane  of  Obliquity  of 
the  earth's  orbit  is  also  slowly  changing  its  position,  and  as  a  the  ecllPtlc 

slowly 

consequence  the  ecliptic  shifts  its  place  among  the  stars,  thus  diminishing, 
slowly  altering  their  latitudes  and  the  angle  between  the  equator 
and  the  ecliptic.     The  obliquity  is  now  about  24'  less  than  it 


144  MANUAL   OF   ASTRONOMY 

was  two  thousand  years  ago,1  and  at  present  is  decreasing  about 

0".5   yearly.      After  about  fifteen  thousand  years,   when  the 

obliquity  will  be  only  22£°,  it  will  begin  to  increase  again  and 

will  "  oscillate  "  like  the  eccentricity.     But  the  whole  change 

can  never  exceed  about  1J°  on  each  side  of  the  mean. 

Slight  peri-         (4)  Periodic  Disturbances  of  the  Earth  in  its  Orbit.     Besides 

odic disturb-  these  "secular  perturbations"  of  the  earth's  orbit,  the   earth 

earth  in         itself  is  all  the  time  slightly  disturbed  in  its  orbit.     On  account 

its  orbit.        of  fa  connection  with  the  moon,  its  center  oscillates  each  month 

a  few  hundred  miles  above  and  below  the  true  plane  of  the 

ecliptic ;  and  by  the  action  of  the  other  planets  it  is  sometimes 

set  forward  or  backward  or  sideways  to  the  extent  of  several 

thousand  miles.     Of  course,  every  such  displacement  of  the 

earth  produces  a  corresponding  slight  change  in  the  apparent 

position  of  the  sun,  and  indeed  of  all  bodies  observed  from  the 

earth,  except  the  moon,  which  accompanies  the  earth,  and  the 

stars,  which  are  too  far  away  to  be  sensibly  affected. 

165.    Precession  of  the  Equinoxes.  —  This  is  a  slow  westward 
Precession      motion  of  the  equinoxes  along  the  ecliptic  first  discovered  by  Hip- 
defined,  its  parchus  about  125  B.C.    He  found  that  the  "year  of  the  seasons," 
Hipparchus.   from  solstice  to  solstice,  as  determined  by  the  gnomon,  was  shorter 
than  that  determined  by  the  heliacal  rising  and  setting  of  the  stars 
(i.e.,  the  times  when  certain  constellations  rise  and  set  with  the 
sun),  just  as  if  the  equinox  "  preceded,"  i.e.,  "  stepped  forward," 
Amount  of     a  little  to  meet  the  sun.    The  difference  between  the  year  of  the 
precession      seasons  and  the  sidereal  year  is  about  twenty  minutes,  the  preces- 
Period^soo  s^on  being  50". 2  yearly,  so  that  the  equinox  makes  the  complete 
years.  circuit  of  the  ecliptic  in  twenty-five  thousand  eight  hundred  years. 

It  is  a  motion  of  the  equator  and  not  of  the  ecliptic  which 

JThe  ancients  determined  the  "obliquity"  with  fair  accuracy  by  observa- 
tions of  the  length  of  the  shadow  of  the  gnomon  at  the  two  solstices.  The 
angle  CBD,  or  SBS'  (Sec.  93,  Fig.  36),  is  twice  the  obliquity.  The  Chinese 
records  contain  an  observation  which  purports  to  be  four  thousand  years  old 
and  is  apparently  genuine. 


THE  ORBITAL  MOTION  OF  THE  EARTH 


145 


causes  the  precession,  as  is  proved  by  the  fact  that  the  latitudes 
of  the  stars  have  changed  but  slightly  in  the  last  two  thousand 
years,  showing  that  the  ecliptic  maintains  its  position  among 
them  nearly  unaltered.  The  right  ascension  and  declination  of 
the  stars,  on  the  other  hand,  are  both  found  to  be  constantly 
changing,  and  this  makes  it  certain  that  it  is  the  celestial  equator 
which  shifts  its  place.  On  account  of  this  change  in  the  place 
of  the  equinox  the  longitudes  of  the  stars  increase  continually, 
—  at  a  sensibly  constant 
rate  of  50".2  a  year, — 
nearly  30°  in  the  last 
two  thousand  years. 

166.  Motion  of  the  Pole 
of  the  Heavens  around 
the  Pole  of  the  Ecliptic. — 
The  obliquity  of  the  eclip- 
tic, which  equals  the  an- 
gular distance  of  the  pole 
of  the  heavens  from  the 
pole  of  the  ecliptic,  is 
not  affected  by  preces- 
sion. That  is  to  say,  as 
the  earth  travels  around 
its  orbit  in  the  plane  of 
the  ecliptic  (just  as  if 
that  plane  were  the  level  surface  of  a  sheet  of  water  in  which 
the  earth  swims  half  immersed),  its  axis,  ACX  (Fig.  55),  always 
preserves  very  nearly  the  same  constant  angle  of  23i°  with  the 
perpendicular,  SCT,  which  points  to  the  pole  of  the  ecliptic. 
But,  in  consequence  of  precession,  the  axis,  while  keeping  its 
inclination  unchanged,  shifts  conically  around  the  line  SCT 
(like  the  axis  of  a  spinning  top),  taking  up  successively  the 
positions  A1C,  AUC,  etc.,  thus  carrying  the  equinox  from  Fto  F', 
and  onwards. 


Due  mainly 
to  motion  of 
the  equator 
as  proved 
by  the  con- 
stancy of  the 
latitudes 
of  stars. 


FIG.  55.  —  Conical  Motion  of  Earth's  Axis 


Revolution 
of  the  pole 
of  the 
heavens 
around  the 
pole  of  the 
ecliptic. 


146 


MANUAL   OF   ASTRONOMY 


In  consequence  of  this  shift  of  the  axis  the  pole  of  the 
heavens,  i.e.,  that  point  in  the  sky  to  which  the  line  CA  happens 
to  be  directed  at  any  time,  describes  a  circle  around  the  pole  of 
the  ecliptic  in  a  period  of  about  twenty-five  thousand  eight 
hundred  years  (360°  -f-  50".2).  While  the  pole  of  the  ecliptic 
has  remained  almost  fixed  among  the  stars,  the  pole  of  the 


Polarii 


84 


x- -»e 


a  Cephei     * 
)0  A.D. 


'—"--(}- 


\  PoZe  o/ 

\ 


a  Cs/grrw 


5  Cygni 


Pole  of  Rotation 
.D. 


-  N  r_  -' 

Eclipfa^D™co 
"  i~"~ 


\  Former 
\Pole  Star 


4600  B.C. 


14  800  A.  D. 


FIG.  56.  —  Processional  Path  of  the  Celestial  Pole 

equator  has  traveled  many  degrees  since  the  earliest  observa- 
tions. Fig.  56  shows  approximately  its  path  among  the  northern 
constellations  ;  not  exactly,  of  course,  on  account  of  the  continual 
slight  shifting  of  the  plane  of  the  earth's  orbit,  which  makes  the 
pole  of  the  ecliptic  move  about  a  little,  so  that  the  center  of  the 
"  precessional  circle  "  is  not  an  absolutely  fixed  point. 


THE  ORBITAL  MOTION  OF  THE  EARTH 


147 


Reckoning  back  about  four  thousand  six  hundred  years,  we  see  from  the 
figure  that  a  Draconis  was  then  the  pole-star,  and  about  five  thousand  six    Former  and 
hundred  years  hence  a  Cephei  will  take  the  office.      The  circle  passes  not   future  pole- 
very  far  from  Vega  on  the  opposite  side  from  the  present  pole-star,  so  that  stars> 
about  twelve  thousand  years  from  now  Vega  (a  Lyrae)  will  be  the  pole- 
star,  —  a  splendid  one  but  rather  inconveniently  far  from  the  pole. 

KB.  —  This  precessional  motion  of  the  celestial  pole  must  not  be  confounded 
with  the  motions  of  the  terrestrial  pole  which  cause  the  variations  of  latitude. 


167.  Displacement  of   the   Signs  of   the  Zodiac.  —  Another 
effect  of  precession  is  that  the  signs  of  the  zodiac  (Sec.  157) 
do  not  now   agree  with 

the  constellations  of  which 
they  bear  the  name.  The 
sign  of  Aries  is  now  in 
the  constellation  of  Pisces, 
and  so  on.  In  the  last 
two  thousand  years  each 
sign  has  backed  bodily, 
so  to  speak,  into  the  con- 
stellation west  of  it. 

Great  changes  have 
taken  place  also  in  the 
apparent  position  of  other  constellations  in  the  sky.  Six  thou- 
sand years  ago  the  Southern  Cross  was  visible  in  England  and 
Germany,  and  Cetus  never  rose  above  the  horizon. 

168.  Physical  Cause  of  Precession.  —  The  physical  cause  of 
this  slow  conical  motion  of  the  earth's  axis  was  first  explained 
by  Newton,  and  lies  in  the  two  facts  that  the  earth  is  not 
exactly  spherical,  but  has,  so  to  speak,  a  protuberant  ring  of 
matter  around  its  equator,  —  the  equatorial  bulge,  —  and  that 
the  sun  and  moon  act  upon  this  ring,  tending  (but  not  able)  to 
draw  the  plane  of  the  equator  into  coincidence  with  the  plane 
of  the  ecliptic,  as  a  magnet  tends  to  draw  the  plane  of  an  iron 
ring  into  line  with  its  pole. 


Effect  of 
precession 
on  the  signs 
of  the 
zodiac. 


FIG.  57.  —  Precession  illustrated  by  the 
Gyroscope 


Mechanical 
explanation 
of  preces- 
sion. 


148 


MANUAL   OF   ASTRONOMY 


Combina- 
tion of 
rotations 
illustrated 
by  the 
gyroscope. 


Why  preces- 
sion is  so 
slow. 


Equation  of 
the  equinox 
due  to  varia- 
tions in  the 
force  which 
produces 
precession. 


If  it  were  not  for  the  earth's  rotation,  this  action  of  the  sun 
and  moon  would  actually  bring  the  two  planes  of  the  equator 
and  ecliptic  into  coincidence ;  but  since  the  earth  is  spinning 
on  its  axis,  we  get  the  same  result  that  we  do  with  the  whirling 
wheel  of  a  gyroscope  by  hanging  a  weight  at  one  end  of  its 
axis  (Fig.  57).  We  then  have  a  combination  of  two  rotations  at 
right  angles  to  each  other,  —  one  the  whirl  of  the  wheel,  the 
other  the  "tip"  which  the  weight  tends  to  give  the  axis.  The 
resultant  effect  —  very  surprising  when  the  experiment  is  seen 
for  the  first  time  —  is  that  the  axis  of  the  wheel,  instead  of 
tipping,  maintains  its  inclination  unchanged,  but  moves  around 
conically  like  the  axis  of  the  earth,  as  shown  in  Fig.  55.  Any 
force  tending  to  change  the  direction  of  the  axis  of  a  whirling 
body  produces  a  motion  exactly  at  right  angles  to  its  own 
direction. 

Compared  with  the  mass  of  the  earth  and  its  energy  of  rota- 
tion, this  disturbing  force  is  very  slight,  and  consequently  the 
rate  of  precession  is  extremely  slow.  If  the  earth  were  spher- 
ical, there  would  be  no  precession.  If  it  revolved  on  its  axis 
more  slowly,  precession  would  be  more  rapid,  as  it  would  be 
also  if  the  sun  and  moon  were  larger  or  nearer,  or  if  the 
obliquity  of  the  ecliptic  were  greater,  not  exceeding  45°. 

The  moon,  being  nearer  than  the  sun,  is  much  the  more 
effective  of  the  two  in  producing  the  precession. 

169.  Equation  of  the  Equinox.  —  The  force  which  tends  to 
pull  the  equator  towards  the  ecliptic  continually  varies.  When 
the  sun  and  moon  are  crossing  the  celestial  equator  the  action 
becomes  zero  —  twice  a  year  for  the  sun,  twice  a  month  for  the 
moon.  Moreover,  as  we  shall  see  (Sec.  192),  the  maximum 
declination  attained  by  the  moon  during  the  month  changes  all 
the  way  from  18°  07'  to  28°  47',  and  its  effect  in  producing 
precession  varies  correspondingly.  As  a  consequence  there  is, 
superposed  upon  the  mean  precession  of  the  equinoxes,  a  small 
periodic  variation  in  its  rate,  producing  the  equation  of  the 


THE   ORBITAL   MOTION   OF   THE   EARTH  149 

equinox,  a  slight  advance  or  recession  of  the  equinox  from 
its  mean  place  never  amounting  to  more  than  a  few  seconds 
of  arc. 

170.  Nutation.  —  This  is  a  slight  motion  of  the  pole  of  the 
equator  alternately  towards  and  from  the  pole  of  the  ecliptic,  —  Nutation  a 
a  "nodding,"  so  to  speak,  of  the  pole.     In  most  positions  of  sli§htperi- 
the  sun  or  moon  with  respect  to  the  equator,  there  is,  in  addi-  motion  of 
tion  to  the  "tipping"  force,  a  slight  thwartwise  action,  tending  the  pole 

to  accelerate  or  retard  the  precession,  just  as  if  one  should  gently  1°™^°* 
draw  horizontally  the  weight  JFat  the  end  of  the  axis  (Fig.  57).  pole  of  the 
The  actual  effect  in  this  case  is  not  to  change  the  rate  of  preces-  ecllptlc- 
sion  in  the  least,  but  to  alter  the  inclination  of  the  axis.     This 
causes  a  nutation  amounting  to  about  9  ".2  as  a  maximum  and 
running  through  its  principal  changes  in  nineteen  years,  —  the 
period  in  which  the  nodes  of  the  moon's  orbit  complete  their 
circuit  (Sec.  192). 

171.  Aberration  of  Light.  —  Aberration1  is  the  apparent  dis-  Aberration 
placement  of  a  heavenly  body,  due  to  the  combination  of  the  orbital 
velocity  of  the  earth  with  the  velocity  of  light. 

The  fact  that  light  is  not  transmitted  instantaneously,  but 
with  a  finite  velocity,  causes  the  displacement  of  an  object 
viewed  from  any  moving  station,  unless  the  motion  is  directly 
towards  or  from  that  object.  If  the  motion  of  the  observer 
is  slow  as  compared  with  the  speed  of  light,  this  displace- 
ment is  insensible  ;  but  the  earth  moves  swiftly  enough  (about 
1  8£  miles  per  second)  to  make  it  easily  observable  with  modern 
instruments.  The  direction  in  which  we  point  our  telescope  to 
observe  a  star  is  usually  not  the  same  as  if  we  were  at  rest,  and 
the  angle  between  the  two  directions  is  the  star's  aberration 
at  the  moment. 

We  may  illustrate  this  by  considering  what  would  happen  in  illustration 
the  case  of  falling  raindrops  observed  by  a  person  in  motion, 


1  It  was  first  discovered  in  1725  (and  later  explained)  by  Bradley,  who  after-    of  .fal 
wards  became  the  English  Astronomer  Royal. 


150 


MANUAL   OF   ASTRONOMY 


Suppose  the  observer  standing  with  a  tube  in  his  hand  while 
the  drops  are  falling  vertically.  If  he  wishes  to  have  the  drops 
descend  through  the  tube  without  touching  the  side,  he  must 
obviously  keep  it  vertical  so  long  as  he  stands  still ;  but  if  he 
advances  in  any  direction,  the  drops  will  strike  his  face  and 
he  will  have  to  draw  back  the  bottom  of  the  tube  (Fig.  58)  by 
an  amount  which  equals  the  advance  he  makes  during  the  time 
while  a  drop  is  falling  through  it ;  i.e.,  he  must  incline  the  tube 
forward  at  an  angle,  a,  which  depends  both  upon  the  velocity 
of  the  raindrop  and  the  velocity  of  his  own  motion,  so  that  when 
the  drop  which  entered  the  tube  at  B  reaches  A'  the  bottom  of 

the  tube  will   be    there    also. 


This    angle 
equation 


is    given   by    the 


'A' 


FIG.  58.  —  Aberration  of  a  Raindrop 


U 

tan  a  =  —  , 

in  which  V  is  the  velocity  of  the 
drop,  and  u  the  velocity  of  the 
observer  at  right  angles  to  V. 

It  is  true  that  this  illustration  is 
not  a  demonstration,  because  light 
does  not  consist  of  particles  coming 
towards  us,  but  of  waves  transmitted 

through  the  ether  of  space.  But  it  has  been  shown  (though  the  proof  is 
by  no  means  elementary)  that,  within  very  narrow  limits,  if  not  exactly, 
the  apparent  direction  of  the  motion  of  a  wave  is  affected  in  precisely  the 
same  way  as  that  of  a  moving  projectile. 

The  constant       172.   The  Constant  of  Aberration.  —  =•  By  the  discussion  of  thou- 

ofaberra-      san(js  of  observations  upon  stars  during  the  past  fifty  years, 

it  is  found  that  the  maximum  aberration  of  a  star  —  the  same 

for  all  stars  —  is  about  20".5,1  which  is  called  the  Constant  of 

Aberration.      This   maximum  displacement  occurs,   of   course, 


value  is  uncertain  by  at  least  0.02  or  0.03  of  a  second.     The  Astro- 
nomical Congress  at  Paris  in  1896  adopted  the  value  20".  47. 


THE   ORBITAL   MOTION   OF   THE   EARTH  151 

whenever  the  sun's  motion  is  at  right  angles  to  the  line  drawn 
from  the  earth  to  the  star,  always  twice  a  year. 

A  star  at  the  pole  of  the  ecliptic  is,  however,  permanently  Aberra- 
in  a  direction   perpendicular  to  the  earth's   motion,  and  will  tlonalorbit 

dftspi*il)f*d 

therefore  always  be  displaced  by  the  same  amount  of  20".5,  but  annually  by 
in  a   direction   continually   changing.     It  therefore   appears   to  each  star, 
describe  during  the  year  as  its  "  aberrational  orbit "  a  little  circle 
41"  in  diameter. 

A  star  on  the  ecliptic  (latitude  0°)  appears  simply  to  oscillate 
back  and  forth  in  a  straight  line  4-1"  long. 

Between  the  ecliptic  and  its  pole  the  aberrational  orbit  is  an 
ellipse  having  its  major  axis  parallel  to  the  ecliptic  and  always 
41"  long,  while  its  minor  axis  depends  upon  the  star's  latitude, 
/3,  and  always  equals  l±lu  sin  @. 

There  is  also  a  very  slight  diurnal  aberration  due  to  the  rotation  of  the 
earth,  its  amount  depending  on  the  observer's  latitude  and  ranging  from 
0".31  at  the  equator  to  zero  at  the  pole. 

173.   Determination  of  the  Earth's  Orbital  Velocity  and  the  Distance  of 
Mean   Distance   of  the   Sun  by  Means  of  Aberration.— From  thesun 

determined 

Sec.  171,  tan  a  =  — ,  which  gives  u  =  V  tan  a,  u  in  this  case  by  means  of 

V  aberration. 

being  the  velocity  of  the  earth  in  its  orbit  and  V  the  velocity 
of  light,  while  a  is  the  constant  of  aberration.     The   experi- 
ments   of   Michelson   and    Newcomb    (Physics,    p.    276)    (con- 
firmed in  1900  by  Perrotin's  experiments  at  Paris  by  a  different  The  meas- 
method)  make  V  equal  186330  miles  a  second,  with  a  probable  uredvelo<^ 
error  of  about  25  miles.     We  have,  therefore,  u,   the  velocity 
of  the  earth  in  its  orbit,  equals  186330  X  tan  20".47  =  18.5 
miles. 

The  circumference  of  the  orbit,  regarded  as  circular  (which  Resulting 
in  the  case  of  the  earth  involves  no  sensible  error),  is  found  valuefor 
by  multiplying  this  velocity,  18.5,  by  the  number  of  mean  distance, 
solar  seconds  in  the  sidereal  year  (Sec.  182).  Dividing  this 


152  MANUAL   OF    ASTRONOMY 

circumference  by  2  IT,  we  find  the  radius  of  the  orbit,  or  the 
mean  distance  of  the  sun,  to  be  very  nearly  92  900000  miles. 

The  uncertainty  of  the  constant  of  aberration  affects  the 
Amount  of     distance  proportionally,  by  perhaps  100000   miles.     Still  the 
uncertainty.   method  is  one  of  the  very  best  of  all  that  we  possess  for  deter- 
mining the  value  of  "  the  astronomical  unit." 

174.   Solar  Time  and  the  Equation  of  Time.  —  Since  the  sun 

makes  the  circuit  of   the  heavens  in  a  year,  moving  always 

Solar  day       towards  the  east,  the  solar  day,  as  has  been  already  explained 

about  four     jn      preceding-  article,  is  about  four  minutes  longer  than  the 

minutes 

longer  than  sidereal  day,  the  difference  amounting  to  exactly  one  day  in  a 
the  sidereal,  year;  i.e.,  while  in  a  sidereal  year  there  are  366  i  (nearly)  sidereal 
days,  there  are  only  365i  solar  days.  Moreover,  the  sun's 
Apparent  advance  in  right  ascension  between  two  successive  noons  varies 
solar  days  materially,  so  that  the  apparent  solar  days  are  not  all  of  the 
unequal  same  length.  December  23  is  fifty-one  seconds  longer  than 
length.  September  16. 

Accordingly,  as  already  explained  (Sec.  98),  mean  time  has 
The  fictitious  been  adopted,  which  is  kept  by  a  "fictitious,"  or  "mean,"  sun 
moving  uniformly  in  the  equator  at  the  same  average  rate  as 
that  of  the  real  sun  in  the  ecliptic.  The  hour  angle  of  this 
mean  sun  is  the  local  mean  time,  or  clock  time,  whUe  the  hour 
angle  of  the  real  sun  is  the  apparent,  or  sun-dial,  time. 

The  Equation  of  time  is  the  difference  between  these  two 
times  reckoned  as  plus  when  the  sun-dial  is  slower  than  the 
clock  and  minus  when  it  is  faster;  i.e.,  it  is  the  correction  which 
must  be  added  (algebraically)  to  apparent  time  in  order  to  get 
mean  time,  and  this  is  simply  equal  to  the  difference  between 
Definition  the  right  ascensions  of  the  fictitious  sun  and  the  true  sun;  so 
°f  ifYlm'"  ^at'  ca^ng  the  e<luation  of  time  E,  we  may  write  E  —  at  —  am, 
in  which  at  is  the  right  ascension  of  the  true  sun  and  am  the 
right  ascension  of  the  mean  sun.  When  at  is  greater  than  an 
the  true  or  real  sun  comes  to  the  meridian  later  than  the  mean 
sun,  and  the  sun-dial  is  slow  of  mean  time. 


THE   ORBITAL   MOTION   OF   THE   EARTH  153 

The  principal  causes  of  this  difference  are  two : 

(1)  The  variable  motion  of  the  sun  in  the  ecliptic,  due  to  the  Causes  of 
eccentricity  of  the  earth's  orbit.  the  equation 

rm  i     •         •  '      7  7  •        •  °f  time> 

(2)  The  obliquity  of  the  ecliptic. 

175.  Effect  of  the  Eccentricity  of  the  Earth's  Orbit. — Near 
perihelion,  which  occurs  about  December  31,  the  sun's  eastward 
motion  on  the  ecliptic  is  most  rapid.     At  this  time,  accordingly, 
the  apparent  solar  days,  for  this  reason,  exceed  the  sidereal  by 

more  than  the  average  amount,  making  the  sun-dial  days  longer  Effect  of  the 

than  the  mean.     The  sun-dial  will  therefore  lose  time  at  this  une^ual 

velocity  of 
season  and  will,  so  far  as  this  cause  is  concerned,  continue  to  the  earth  in 

do  so  until  the  motion  of  the  sun  falls  to  its  average  value,  as  different 
it  will  at  the  end  of  three  months ;  at  this  time  the  difference  orbit,  pro- 
will  have  amounted  to  about  7|  minutes.     Then  the  sun-dial  ducingan 
will  gain  until  aphelion,  and  at  that  time  the  clock  and  sun-  l^^n 
dial  will  once  more  agree.     During  the  remaining  half  of  the  minutes, 
year  the  action  will  be  reversed.     The  equation  of  time,  there- 
fore, so  far  as  due  to  this  cause  only,  is  about  4-  7f  minutes  in 
the  spring,  and  —  7f  in  the  autumn. 

176.  Effect  of  the  Obliquity  of  the  Ecliptic.  —  Even  if  the  Equation 
sun's  motion  in  longitude  (i.e.,  along  the  ecliptic)  were  uniform,  ^{j^f^f 
its  motion  in  right  ascension  would  be  variable.     If  the   true  the  ecliptic, 
and  fictitious  suns  were  together  at  the  vernal  equinox,  one 
moving  uniformly  in  the  ecliptic  and  the  other  in J;he  equator, 

they  would  indeed  be  together  (i.e.,  have  the  same  right  ascen-  Uniform 
sions)  at  the  two  solstices  and  at  the  other  equinox,  because  it  motlon°f 

sun  on  the 

is  just  180°   from   equinox   to   equinox  and  the  solstices  are  ecliptic  does 
exactly  half-way  between  them  ;  but  at  any  point  between  the  r  ot  glve  a 
solstices  and  equinoxes  their  right  ascensions  would  differ.  motion  in 

This  is  easily  seen  by  taking  a  celestial  globe  and  marking  r|ght 
on  the  ecliptic  the  point  m  (Fig.  59),  half-way  between  the 
vernal  equinox  E  and  the  summer  solstice  C,  and  also  marking 
a  point  n  on  the  equator  45°  from  the  equinox.     It  will  be  seen 
at  once  that  the  former  point  is  west  of  n,  the  difference  of 


154 


MANUAL   OF   ASTRONOMY 


Equation  of 
time  due  to 
this  cause 
about  + 10m 
six  weeks 
before  each 
equinox, 
and  -10™ 
six  weeks 
after  it. 


Graphical 
combination 
of  the  two 
components 
of  the  equa- 
tion of  time, 
showing  the 
total  result 
and  effect. 


right  ascension  being  m'n,  so  that  m  in  the  apparent  diurnal 
revolution  of  the  sky  will  come  first  to  the  meridian.1  In  other 
words,  about  six  weeks  after  each  equinox,  when  the  sun  is  half- 
way between  the  equinox  and  the  solstice,  the  sun-dial,  so  far 
as  the  obliquity  of  the  ecliptic  is  concerned,  is  faster  than  the  clock, 
and  this  component  of  the  equation  of  time  is  minus,  amounting 
to  nearly  ten  minutes.  Of  course,  the  same  thing  holds,  with 
the  necessary  changes,  for  the  other  quadrants. 

If  the  ecliptic  be  divided  into  equal  portions  from  E  to  C 
and  hour-circles  be  drawn  from  P  through  the  points  of  division, 
it  is  clear  that  near  E  the  portions  of  the  ecliptic  are  longer 

than  the  corresponding  portions 
of  the  equator.  On  the  other 
hand,  near  the  solstice  C  the 
arc  of  the  ecliptic  is  shorter 
than  the  corresponding  arc  of 
the  equator,  on  account  of  the 
divergence  of  the  hour-circles  as 
they  recede  from  the  pole. 

177.   Combination  of    the 
FIG  59  Effects  of  the  Two  Causes.  - 

We  can  represent  the  two  com- 
ponents of  the  equation  of  time  and  the  result  of  their  combi- 
nation by  a  graphical  construction  (Fig.  60). 

The  central  horizontal  line  is  a  scale  of  dates  one  year  long, 
the  months  being  indicated  at  the  top.  The  dotted  curve  shows 
that  component  of  the  equation  of  time  which  is  due  to  the 
eccentricity  of  the  earth's  orbit.  In  the  same  way  the  broken- 
line  curve  denotes  the  effect  of  the  obliquity  of  the  ecliptic. 
The  heavy-line  curve  represents  the  combined  effect  of  the  two 


1  In  the  figure  the  observer  is  supposed  to  be  looking  at  the  globe  from  the 
west,  E,  the  vernal  equinox,  being  at  the  west  point  of  the  horizon.  EGA  is 
the  ecliptic,  its  pole  being  K ;  while  EQAT  is  the  celestial  equator,  its  pole 
(of  diurnal  rotation)  being  P. 


THE   ORBITAL   MOTION   OF   THE    EARTH  155 


Q-  •- 


\ 


TO 


156 


MANUAL   OF   ASTRONOMY 


Other  causes 
contribute 
slightly  to 
the  equation 
of  time. 

Dates  when 
equation 
of  time 
becomes 
zero. 


causes,  its  ordinate  at  each  point  being  made  equal  to  the 
algebraic  sum  of  the  ordinates  of  the  other  two  curves.  The 
heavy-line  curve  is  carefully  laid  out  from  the  Nautical  Almanac 
for  1902  (a  mean  year  in  the  "leap-year  cycle")  and  will  give 
the  equation  of  time  for  any  date  during  the  next  fifty  years 
within  less  than  half  a  minute ;  not  exactly,  because  from  year 
to  year  the  equation  of  time  for  any  day  of  the  month  varies 

Autumnal  Equinox 


Vernal  Equinox 

FIG.  61.  —  The  Seasons 

a  few  seconds.  The  small  rectangles  reckoned  horizontally 
represent  fifteen-day  intervals;  vertically,  intervals  of  five 
minutes. 

The  two  causes  discussed  above  are  only  the  principal  ones. 
Every  perturbation  suffered  by  the  earth  slightly  modifies  the 
result,  but  all  other  causes  combined  never  affect  the  equation 
of  time  by  as  much  as  ten  seconds. 

The  equation  of  time  becomes  zero  four  times  yearly,  as  will 
be  seen  from  the  figure,  —  about  April  15,  June  14,  Septem- 
ber 1,  and  December  24 ;  but  the  dates  vary  a  little  from  year 
to  year. 


THE   ORBITAL  MOTION   OF   THE   EARTH  157 

178.  The  Seasons.  —  The  earth  in  its  orbital  motion  keeps  its 
axis  nearly  parallel  to  itself  for  the  same  mechanical  reason 
that  a  spinning  globe  maintains  the  direction  of  its  axis  unless 
disturbed  by  some  outside  force,  —  very  prettily  illustrated  by 
the  gyroscope.     Since   this  axis   is  not  perpendicular  to  the 

plane  of  its  orbit,  the  poles  of  the  earth  vary  in  their  presenta-  Alternate 
tion  to  the  sun,  as  shown  in  Fig.  61.     At  the  two  equinoxes,  Presentation 
March  21  and  September  22,  the  plane  of  the  earth's  equator  south  poles 
passes  through  the  sun,  so  that  the  circle  which  divides  day  of  the  earth 
from  night  upon  the  earth  passes  through  the  pole,  as  shown  in 
Fig.  62,  B,  and  day  and  night  are  then  everywhere  equal.     On 
June  21  the  earth  is  so  situated  that  its  north  pole  is  inclined 
towards  the  sun  by  about  23i°,  as  shown  in  Fig.  62,  A.     The 
south  pole  is  then  in  the  unillumi- 
nated  half  of  the  globe,  while  the 
north  pole  receives  sunlight  all  day 
long ;  and  in  all  portions  of  the  north- 
ern  hemisphere    the  day  is  longer 
than  the  night,  arid  vice  versa  in  the 
southern  hemisphere.     At  the  time        FIG.  62. -Position  of  Pole  at 

Solstice  and  Equinox 

of  the  winter  solstice  these  condi- 
tions   are   reversed   and   the   south   pole   has   perpetual   sun- 
shine.    On  the  equator  day  and  night  are  equal  at  all  times 
of  the  year,  and  there  are  no  seasons  in  the  proper  sense  of 
the  word. 

The  midnight  sun  and  other  phenomena  in  the  neighborhood  Station  in 
of  the  pole  have  already  been  discussed  (Sec.  36).  hemfsTere 

179.  Effects  on  Temperature.  —  The  changes  in  the  duration  receives 
of  insolation  (exposure  to  sunshine)  at  any  place  involve  changes  more  tban 
of  temperature  and  of  other  climatic  conditions  which  produce  amount  Of 
the  seasons.     Taking  as  a  standard  the  average  amount  of  heat  heat  in  a 
received  from  the  sun  in  twenty-four  hours  on  the  day  of  the  ^^0^11 
equinox,  it  is  clear  that  the  surface  of  the  soil  at  any  place  in  of  equator, 
the  northern  hemisphere  will  receive  each  twenty-four  hours 


158 


MANUAL   OF   ASTRONOMY 


more  than  the  average  of  heat  whenever  the  sun  is  north  of  the 
celestial  equator,  and  for  two  reasons : 

(1)  Sunshine  lasts  more  than  half  the  day. 

(2)  The  mean  altitude  of  the  sun  while  above  the  horizon  is 
greater  than  at  the  time  of  the  equinox. 

Now  the  more  obliquely  the  rays  strike  the  less  heat  they 
bring  to  each  square  inch  of  the  surface,  as  is  obvious  from 
Fig.  63.  A  beam  of  sunshine  having  a  cross-section,  ABCD, 
is  spread  over  a  larger  area  when  it  strikes  obliquely  than  when 
vertically,  its  heating  efficiency  being  in  inverse  ratio  to  the 
surface  over  which  the  heat  is  distributed.  If  Q  is  the  amount 
of  heat  per  square  meter  of  area  brought  by  the  rays  when  fall- 
ing perpendicularly,  as  on  the  sur- 
face AC,  then  on  Ac,  on  which  it 
strikes  at  the  angle  h  (equal  to  the 
sun's  altitude),  the  amount  per 
square  meter  will  be  only  Q  X  sin  h. 
Moreover,  this  difference  in  favor 
of  the  more  nearly  vertical  rays  is 
FIG.  63. -Effect  of  Sun's  Elevation  exaggerated  by  the  absorption  of 
on  Amount  of  Heat  imparted  to  heat  in  the  atmosphere,  since  ravs 

the  Soil  J 

that  are  nearly  horizontal  have  to 

traverse  a  much  greater  thickness  of  air  before  reaching  the 
ground. 

For  these  two  reasons,  therefore,  at  a  place  in  the  northern 
hemisphere  the  mean  temperature  of  the  day  rises  rapidly  as 
the  sun  comes  north  of  the  equator,  thus  causing  summer. 

180.  Time  of  Highest  Temperature.  —  We  receive  the  most 
heat  in  twenty-four  hours  at  the  time  of  the  summer  solstice ; 
but  this  is  not  the  hottest  time  of  the  season  for  the  obvious 
reason  that  the  weather  is  still  getting  hotter,  and  the  maxi- 
mum will  not  be  reached  until  the  increase  ceases;  i.e.,  not 
until  the  amount  of  heat  lost  in  twenty-four  hours  equals  that 
received,  which  occurs  in  our  latitude  about  August  1,  For 


THE  ORBITAL  MOTION  OF  THE  EARTH      159 

similar  reasons    the    minimum    temperature   of   winter  occurs 
about  February  1. 

Since  the  weather  is  not  entirely  "  made  on  the  spot  where 
it  is  used,"  but  is  much  influenced  by  winds  and  currents  that 
come  from  great  distances,  the  actual  date  of  the  maximum  tem- 
perature at  any  particular  place  cannot  be  determined  beforehand 
by  mere  astronomical  considerations,  but  varies  considerably 
from  year  to  year.  The  great  differences  between  the  seasons 
of  different  years  are  as  yet  mostly  without  explanation. 

181,    Difference  between  Seasons  in  Northern  and  Southern  Effect  of  the 
Hemispheres.  —  Since  in  December  the  distance  of  the  earth  eccentricity 
from  the  sun  is  about  three  per  cent  less  than  it  is  in  June,  the  earth's  orbit 
earth  as  a  whole  receives  hourly  about  six  per  cent  more  heat  in  producing 
in  December  than  in  June,  the  heat  received  varying  inversely  between  th« 
as  the  square  of  the  distance.     For  this  reason  the  southern  seasons  in 
summer,  which  occurs  in  December  and  January,  is  hotter  than  and^outh6-" 
the  northern.     It  is,  however,  seven  days  shorter,  because  the  em  hemi- 
earth  moves  more  rapidly  in  that  part  of  its  orbit.     The  total  8pbe 
amount  of  heat  per  acre  received  during  the   whole  summer 
is  therefore  sensibly  the  same  in  each  hemisphere,  the  short- 
ness   of   the    southern    summer   making   up    for  its  increased 
warmth. 

The  southern  winter,  however,  is  both  longer  and  colder  than  Question 
the  northern,  and  it  has  been  vigorously  maintained  by  certain  whether  the 
geologists  that,  on  the  whole,  the  mean  annual  temperature  of  period  can 
the  hemisphere  which  has  its  winter  at  the  time  when  the  earth  be  explained 
is  in  aphelion  is  lower  than  the   opposite  one.     It  has  been  effect, 
attempted  to  account  for  the  glacial  epochs  in  this  way,  but  the 
explanation  is  very  doubtful. 

On  account  of  the  motion  of  the  apsides  of  the  earth's  orbit 
(Sec.  164)  the  present  state  of  things  will  be  reversed  in  about 
ten  thousand  years ;  the  perihelion  will  then  be  reached  in 
June,  and  the  northern  summer  will  then  be  the  shorter  and 
the  hotter  one. 


160  MANUAL   OF   ASTRONOMY 

182.  The  Three  Kinds  of  Year.  —  Three  different  kinds  of 
"  year  "  are  now  recognized,  —  the  sidereal,  the  tropical  or  equi- 
noctial, and  the  anomalistic. 

The  Sidereal  Tear,  as  its  name  implies,  is  the  time  occu- 
pied by  the  sun  in  apparently  completing  the  circuit  of  the 
heavens  from  a  given  star  to  the  same  star  again.  Its  length  is 
365d6h9m98  of  mean  solar  time  (365d.25636). 

From  the  mechanical  point  of  view  this  is  the  true  year ;  i.e., 
it  is  the  time  occupied  by  the  earth  in  making  one  complete 
revolution  around  the  sun  from  a  given  direction  in  space  to 
the  same  direction  again. 

The  Tropical  Year  is  the  time  included  between  two  suc- 
cessive passages  of  the  vernal  equinox  by  the  sun.  On  account 
of  precession  (Sec.  165)  the  equinox  moves  yearly  50". 2  towards 
the  west,  so  that  the  tropical  year  is  shorter  than  the  sidereal, 
its  length  being  365d5h48m458.5  (365d.24219).  Its  length  was 
determined  by  the  ancients  with  considerable  accuracy,  as  365 i 
days,  by  means  of  the  gnomon ;  they  noted  the  dates  at  which 
the  noonday  shadow  was  longest  (or  shortest),  i.e.,  the  date  of 
the  solstice. 

Since  the  seasons  depend  on  the  sun's  place  with  respect  to 
The  tropical  the  equinox,  the  tropical  year  is  the  year  of  chronology  and 


year  the         civj}  reckoning.     Whenever  a  period  of  so  many  years  is  spoken 
chronology,    of  we  always  understand  tropical  years,  unless  otherwise  dis- 
tinctly indicated. 

The  anoma-        The  third  kind  of  year  is  the  Anomalistic  Year,  —  the  time 
listicyear,—  between  two  successive  passages  of  the  perihelion.     Since  the 

365  25958 

days  line  of  apsides  of  the  earth's  orbit  moves  eastward  about  11"  a 

year  (Sec.  164),  this  kind  of  year  is  nearly  five  minutes  longer 
than  the  sidereal,  its  length  being  365d6h13m488  (365d.25958). 

It  is  little  used,  except  in  calculations  relating  to  perturba- 
tions. 

183.  The  Calendar.  —  The  natural  units  of  time  are  the  day, 
month,  and  year.  The  day  is  too  short  for  convenience  in 


THE   ORBITAL   MOTION   OF   THE   EARTH  161 

dealing  with  considerable  periods,  —  such  as  the  life  of  a  man, 
for  instance  ;  and  the  same  is  true  even  of  the  month,  so  that 
for  all  chronological  purposes  the  tropical  year  —  the  year  of 
the  seasons  —  has  always  been  employed.  At  the  same  time,  so 
many  religious  ideas  and  observations  have  been  connected  with 
the  changes  of  the  moon  that  there  was  long  a  constant  struggle  to 
reconcile  the  month  with  the  year.  Since  the  two  are  incommen- 
surable, no  really  satisfactory  solution  is  possible,  and  the  modern 
calendar  of  civilized  nations  entirely  disregards  the  moon. 

In  the  ancient  times  the  calendar  was  in  the  hands  of  the  priesthood 
and  was  predominantly  lunar,  the  seasons  either  being  disregarded  or  kept   Lunar 
roughly  in  place  by  the  occasional  intercalation  or  dropping  of  a  month,    calendars. 
The  principal  Mohammedan  nations  still  use  a  purely  lunar  calendar  having 
a  year  of  twelve  lunar  months  containing  alternately  354  and  355  days.    In 
their  reckoning,  therefore,  the  months  and  their  religious  festivals  fall  con- 
tinually in  different  seasons,  and  their  calendar  gains  on  ours  about  one 
year  in  thirty -three. 

184.  The  Julian  Calendar.  —  When  Julius  Caesar  came  into 
power  he  found  the  Roman  calendar  in  a  state  of  hopeless  con- 
fusion. He  therefore  sought  the  advice  of  the  Alexandrian 
astronomer  Sosigenes,  and  in  accordance  with  his  suggestions 
established  (45  B.C.)  what  is  known  as  the  Julian  calendar,  The  Julian 
which  still,  either  untouched  or  with  a  trifling  modification,  calendar: 

every  fourth 

continues  in  use  among  all  civilized  nations.     He  discarded  all  year  a  leap- 
consideration  of  the  moon,  and  adopting  365^  days  as  the  true  year- 
length  of  the  year,  he  ordained  that  every  fourth  year  should 
contain  366  days,  the  extra  day  being  inserted  by  repeating  the 
sixth  day  before  the  calends  of  March,  whence  such  a  year  is 
called  bissextile.    He  also  transferred  to  January  1  the  begin-  Whyieap- 
ning  of  the  year,  which  until  then  had  been  in  March  (as  is  f<e£* 
indicated  by  the  names  of  several  of  the  months,  as  September,  tile. 
i.e.,  the  seventh  month,  etc.). 

Csesar  also  took  possession  of  the  month  Quintilis,  naming 
it  July  after  himself.     His  successor,  Augustus,  in  a  similar 


162 


MANUAL   OF   ASTRONOMY 


Incorrect- 
ness of  the 
Julian 
calendar. 


The  Grego- 
rian calen- 
dar. Correc- 
tion made, 
and  error 
prevented 
from  accu- 
mulating by 
new  rule 
respecting 
leap-year. 


Adoption  of 
the  Grego- 
rian calen- 
dar in  Eng- 
land in  1752. 


manner  appropriated  the  next  month,  Sextilis,  calling  it  August, 
and  to  vindicate  tys  dignity  and  make  his  month  as  long  as  his 
predecessor's  he  added  to  it  a  day  stolen  from  February. 

The  Julian  calendar  is  still  used  unmodified  in  Russia  and 
by  the  Greek  Church  generally. 

185.  The  Gregorian  Calendar.  —  The  true  length  of  the  tropi- 
cal year  is  not  365i  days,  but  365d5h48m458.5,  leaving  a  differ- 
ence of  Hm148.5  by  which  the  Julian  year  is  too  long.     This 
amounts  to  a  little  more  than  three  days  in  four  hundred  years. 
As  a  consequence,  in  the  Julian  calendar  the  date  of  the  vernal 
equinox  comes  earlier  and  earlier  as  time  goes  on,  and  in  1582 
it  had  fallen  back  to  the  llth  of  March  instead  of  occurring 
on  the  21st,  as  it  did  at  the  time  of  the  Council  of  Nice,  A.D.  325. 
Pope  Gregory,  therefore,  under  the  advice  of  the  distinguished 
astronomer  Clavius,  ordered  that  the  calendar  should  be  cor- 
rected by  dropping  ten  days,  so  that  the  day  following  Oct.  4, 
1582,  should  be  called  the  15th  instead  of  the  5th  ;  and  further, 
to  prevent  any  future  displacement  of  the  equinox,  he  decreed 
that  thereafter  only  such  century  years  should  be  leap-years  as 
are  divisible  by  400.     (Thus,  1700, 1800, 1900,  2100,  and.so  on, 
are  not  leap-years,  while  1600  and  2000  are.) 

186.  The  change  was  immediately  adopted  by  all  Catholic 
countries,  but  the  Greek  Church  and  most  Protestant  nations 
refused  to  recognize  the  Pope's  authority.     It  was,  however, 
finally  adopted  in  England  by  an  act  of  Parliament,  passed  in 
1751,  providing  that  the  year  1752  should  begin  on  January  1 
(instead  of  March  25,  as  had  long  been  the  rule  in  England) 
and  that  the  day  following  Sept.  2,  1752,  should  be  reckoned 
as  the  14th  instead  of  the  3d,  thus  dropping  eleven  days. 

The  change  was  bitterly  opposed  by  many,  and  there  were  riots  in  conse- 
quence in  various  parts  of  the  country,  especially  at  Bristol,  where  several 
persons  were  killed.  The  cry  of  the  people  was,  "  Give  us  back  our  fort- 
night," for  they  supposed  they  had  been  robbed  of  eleven  days,  although 
the  act  of  Parliament  was  carefully  framed  to  prevent  any  injustice  in  the 
collection  of  interest,  payment  of  rents,  etc. 


THE   ORBITAL   MOTION    OF    THE    EARTH  163 

At  present,  since  the  years  1800  and  1900  were  leap-years  in 
the  Julian  calendar  and  not  in  the  Gregorian,  the  difference 
between  the  two  calendars  is  thirteen  days;  thus,  in  Russia  the  Present 
22d  of  June  is  reckoned  the  9th,  but  in  that  country  both  dates  d5erence  of 

*  the  two 

are  ordinarily  used  for  scientific  purposes,  so  that  the  date  would  calendars  is 
be  written  June  ^.  d^TTnd 

When  Alaska  was  annexed  to  the  United  States  the  official  wjn  remain 
date  had  to  be  changed  by  only  eleven  days,  one  day  being  so  until  the 
provided  for  in  the  alteration  from  the  Asiatic  reckoning  to  the 
American  (Sec.  111). 

187.  The  Metonic  Cycle  and  Golden  Number.  —  In  establishing 
a  relation  between  the  solar  and  lunar  years,  the  discovery  of 

the  so-called  lunar  (or  Metonic)  cycle  by  Meton,  about  433  B.C.,  The  Metonic 
considerably  simplified  matters.      This   cycle   consists  of   235  n^e^~n 
synodic  months  (from  new  moon  to  new  again),  which  is  very  years—  very 
approximately  equal  to  nineteen  common  years  of  365  J  days.  nearly  e<iual 
The  calendar  for  the  phases  of  the  moon  is,  therefore  (with  very  months. 
rare  exceptions),  the  same  for  any  two  years  nineteen  years  apart; 
i.e.,  the  calendar  of  the  phases  of  the  moon,  and  of  all  ecclesias- 
tical holidays  which  depend  upon  them  (Easter,  etc.),  is  the 
same  for  1901  as  for  1882  and  1920.     But  the  dates  are  liable 
to  a  shift  of  a.  single  day,  according  to  the  number  of  leap-years 
which  intervene.     This  cycle  is  still  employed  in  the  ecclesias- 
tical calendar  in  determining  the  time  of  Easter. 

The  golden  number  of  a  year  is  its  number  in  this  Metonic  The  "golden 
cycle  and  is  found  by  adding  1  to  the  date  number  of  the  year  number-" 
and  dividing  by  19.     The  remainder,  unless  zero,  is  the  golden 
number.     If  it  comes  out  zero,  19  is  taken.     Thus,  the  golden 
number  for  the  year  1902  is  3. 

188.  The  Julian  Period  and  Julian  Epoch.  —  The  Julian  Period  The  Julian 


consists  of  7980  Julian  years  (28  X  19  X  15),  each  contain-  P61™1  and 

J  v  epoch  intro- 

ing    exactly    365  i    days,   and  its  starting-point,  or  Epoch,   is  ducedbyj. 
Jan.  1,  4713  B.C.,  —  the  Julian  date  of  Jan.  1,  A.D.  1,  being  Scaiiger. 
J.E.  4714. 


164 


MANUAL    OF    ASTRONOMY 


The  system  was  proposed  by  J.  Scaliger  in  1582  as  a  uni- 
versal harmonizer  of  the  different  systems  of  chronological 
reckoning  then  in  use,  and  its  adoption  has  brought  order  out 
of  confusion.  It  is  extensively  employed  in  astronomical  calcu- 
lations, the  date  of  any  phenomenon  being  expressed  beyond  all 
ambiguity  either  by  the  (Julian)  year  and  day,  or  still  more 
simply  by  "  day  number  "  so  and  so  of  the  Julian  era.  Thus,  the 
date  of  the  solar  eclipse  of  Aug.  9, 1896,  is  J.E.  6609,  222d  day, 
or  simply  Julian  day  2  413781 ;  and  this  is  perfectly  definite  to 
every  astronomer  of  whatever  nation,  —  American,  Russian, 
Arabian,  or  Chinese. 

The  number  of  days  between  any  two  events,  even  centuries 
apart,  is  at  once  found  by  merely  taking  the  difference  between 
their  Julian  day  numbers. 

The  Almanac  gives  for  each  year  its  Julian  number,  and  also  the  Julian 
day  number  for  January  1  of  that  year. 

1900  is  Julian  year  6613.     Jan.        1,  1900,  is  Julian  day  2  415021. 
1902"       «          «     6615.       «  1,1902,"       «         «    2415751. 

March  10,  1902,  «       «         «    2  415820,  etc. 

For  a  fuller  explanation  of  the  considerations  on  which  this  system 
of  reckoning  is  founded,  the  reader  is  referred  to  Herschel's  Outlines  of 
Astronomy,  Art.  924. 

EXERCISES 

1.  What  is  the  meridian  altitude  of  the  sun  at  Princeton  (Lat.  40°21/) 
on  the  day  of  the  summer  solstice  ? 

2.  What  is  the  sun's  approximate  right  ascension  at  that  time  ? 

3.  On   what  days  during  the  year  will  the   sun's  right  ascension  be 
approximately  an  even  hour  (i.e.,  0  hours,  2  hours,  4  hours,  etc.)  ? 

4.  On  what  days  will  it  be  an  odd  hour? 

5.  What  is  the  (approximate)  sidereal  time  at  10  P.M.  on  May  12  ? 

Ans.    13h26m. 

6.  At  what  time  will  Arcturus  (R.A.  =  14h10m)  come  to  the  meridian 
on  August  1?  Ans.    About  5h26m  P.M. 

7.  About  what  time  of  night  is  Mizar  (R.A.  =  13h20m)  vertically  under 
the  pole  on  October  10  ?  Ans.   Midnight. 


THE   ORBITAL   MOTION    OF    THE    EARTH  165 

8.  In  what  latitude  has  the  sun  a  meridian  altitude  of  80°  on  June  21  ? 

Ans.    +  33°  27'. 

9.  What  are  the  longitude  arid  latitude  (celestial)  of  the  north  celestial 
pole?  Ans.    Long.  90°,  Lat.  66°  33'. 

10.  What  are  the  right  ascension  and  declination  of  the  north  pole  of 
the  ecliptic?  Ans.    R.A.  18h,  Dec.  66°  33'. 

11.  What  are  the  greatest  and  least  angles  made  by  the  ecliptic  with 
the  horizon  at  New  York  (Lat.  40°  43')  ? 

Ans.     *•-  40"  «•*»*  »<- 


12.  Does  the  vernal  equinox  always  occur  on  the  same  day  of  the 
month?     If  not,  why  not?     How  much  can  the  date  vary? 

13.  Will  the  ephemeris  of  the  sun  for  one  year  be  correct  for  every 
other  year,  and,  if  not,  how  much  can  it  be  in  error  ? 

Ans.    A  difference  of  If  days'  motion  of  the  sun  is  possible  ;  as,  for 
instance,  between  1897  and  1903,  the  leap-year  being  omitted  in  1900. 

14.  When  the  sun  is  in  the  sign  of  Cancer  in  what  constellation  is  he? 

15.  What  obliquity  of  the  ecliptic  would  reduce  the  width  of  the  tem- 
perate zone  to  zero  ? 

16.  At  a  place  west  of  Philadelphia  an  observer  finds  that  his  local 
apparent  time  on  October  1,  as  determined  from  the  sun  by  sextant,  was 
8m3Q8  siow  of  eastern  standard  time.     The  equation  of  time  on  that  date 
is  -  10m88.     What  was  his  longitude  from  Greenwich  ?       Ans.    5h18m388. 

17.  At  what  standard  time  will  the  sun  come   to   the  meridian  on 
March  21  at  Boston  (Long.  4h44m  west  of  Greenwich),  the  equation  of 
time  being  +  7m288?  Ans.    Ilh51m28». 

18.  When  the  equation  of  time  is  16  minutes,  as  it  is  on  November  1, 
how  does  the  forenoon  from  sunrise  till  12  o'clock  compare  in  length  with 
the  afternoon  from  12  o'clock  till  sunset? 

19.  Why  do  the  afternoons  begin  to  lengthen  about  December  8,  a  fort- 
night before  the  winter  solstice  ? 

20.  There  were  five  Sundays  in  February,  1880.     The  same  thing  has 
not  occurred  since,  and  will  not  until  when  ?  Ans.    1920. 

21.  What  was  the  Russian  date  corresponding  to  Feb.  28,  1900,  in  our 
calendar?     What  corresponding  to  May  1  of  the  same  year? 

Ans.    February  16;  April  18. 


CHAPTER   VII 


Importance 
of  the 
moon  in 
astronomy. 


Apparent 
motion  of 
the  moon 
among  the 

stars. 


THE   MOON 

The  Moon's  Orbital  Motion  and  the  Month  —  Distance,  Dimensions,  Mass,  Density, 
and  Force  of  Gravity  —  Rotation  and  Librations  —  Phases  —  Light  and  Heat  — 
Physical  Condition  —  Telescopic  Aspect  and  Peculiarities  of  the  Lunar  Surface 

189.  Next  to  the  sun,  the  moon  is  the  most  conspicuous  and 
to  us  the  most  important  of  the  heavenly  bodies,  —  in  fact,  the 
only  one  except  the  sun  which  exerts  the  slightest  influence 
upon   human  life.      If  the  stars   and  planets  were   all  extin- 
guished, our  eyes  would  miss  them,  and  that  is  all ;  but  if  the 
moon  were  annihilated,  the  interests   of  commerce  would  be 
seriously  affected  by  the  practical  cessation  of  the  tides.     She 
owes  her  conspicuousness  and  importance,  however,  solely  to  her 
nearness,  for  she  is  really  a  very  insignificant  body  as  compared 
with  the  stars  and  the  planets. 

And  yet,  astronomically,  she  perhaps  ranks  highest  among 
the  heavenly  bodies.  The  very  beginnings  of  the  science  seem 
to  have  originated  in  the  study  of  her  motions  and  of  the  differ- 
ent phenomena  which  she  causes,  such  as  the  eclipses  and  the 
tides;  and  in  the  development  of  modern  theoretical  astron- 
omy the  "  lunar  theory,"  with  the  problems  it  raises,  has  been 
perhaps  the  most  fertile  field  of  discovery  and  invention. 

190,  The  Moon's  Apparent  Motion;  Definition  of  Terms,  etc. 
—  One   of   the  earliest   observed  of   astronomical   phenomena 
must  have  been  the  eastward  motion  of  the  moon  with  reference 
to  the  sun  and  stars  and  the  accompanying  changes  of  phase. 
If  we  note  the  moon  to-night  as  very  near  some  conspicuous 
star,  we  shall  find  her  to-morrow  night  at  a  point  about  13° 
farther  east,  and  the  next  night   as  much  farther   still;  she 

166 


THE   MOON  167 

makes  a  complete  circuit  of  the  heavens,  from  star  to  star 
again,  in  about  27£  days.  In  other  words,  she  "revolves 
around  the  earth"  in  that  time,  while  she  accompanies  us  in 
our  annual  journey  around  the  sun. 

Since  the  moon  moves  eastward  among  the  stars  so  much  The  moon's 
faster  than  the  sun,  she  overtakes  and  passes  him  at  regular  aPParent 

motion  with 

intervals ;  and  as  her  phases  depend  upon  her  apparent  position  respect  to 
with  respect  to  the  sun,  this  interval  from  new  moon  to  new  thesun- 

The 

moon  is  specially  noticeable  and  is  what  we  ordinarily  under-  month. 
stand  as  the  month,  —  technically,  the  synodic  month. 

The  Elongation  of  the  moon  is  her  angular  distance  east  or  Definitions 
west  of  the  sun  at  any  time.     At  new  moon  it  is  zero,  and  the  of  elon&a~ 

tion,  con- 
niOOn  is  said  to  be  in    Conjunction.     At  full  moon  the  elon-  junction, 

gation  is  180°,  and  she  is  said  to  be  in   Opposition.     In  both  etc> 
cases  the  moon  is  in  Syzygy,  i.e.,  the  sun,  moon,  and  earth  are 
ranged  nearly  along  a  straight  line.     When  the  elongation  is 
90°  she  is  said  to  be  in  Quadrature. 

191.    Sidereal  and  Synodic   Months.  —  The    Sidereal   Month  The  sidereal 
is  the  time  it  takes  the  moon  to  make  her  revolution  from  a  and  ^nodlc 

months. 

given  star  to  the  same  star  again  as  seen  from  the  center  of 
the  earth.  It  averages  27d7M3mll8.55  (27d.32166),  but  it  varies 
some  three  hours  on  account  of  "perturbations."  The  mean 
daily  motion  is  360°  -J-  27.32166,  or  13°  II'.  Mechanically 
considered,  the  sidereal  month  is  the  true  month. 

The  synodic  month  is  the  time  between  two  successive  con- 
junctions or  oppositions,  i.e.,  between  successive  new  or  full 
moons.  Its  average  value  is  29d12h44m28.86,  but  it  varies 
nearly  thirteen  hours,  mainly  on  account  of  the  eccentricity  of 
the  lunar  orbit.  As  has  been  said  already,  this  synodic  month 
is  what  we  ordinarily  mean  when  we  speak  of  a  "  month." 

If  M  be  the  length  of  the  moon's  sidereal  period,  E  the  length  Relation 
of  the  sidereal  year,  and  S  that  of  the  synodic  month,  the  three  between  the 

J  ^  sidereal  and 

quantities  are  connected  by  a  very  simple  relation.     —  is  the  synodic 

J  J  M  months. 


168 


MANUAL   OF   ASTRONOMY 


fraction  of  a  circumference  moved  over  by  the  moon  in  a  day. 

Similarly,  —  is   the  apparent  daily  motion  of  the  sun.     The 
JS 

difference  is  the   amount  which  the  moon  gains  on  the  sun 
daily.     Now  it  gains  a  whole  revolution  in  one  synodic  month 

of  S  days,  and  therefore  must  daily  gain  —  of  the  circumference. 
Equation  of    Hence,  we  have  the  important  equation  —  -  -  —  =  —  ,  "the  equa- 

synodic 

motion.  »  ,.  ..        ,,      -,  ~ 

tion  of  synodic  motion,    whence  S  = 


M 
X 


Number  of 
sidereal 
months  in  a 
year  exactly 
one  more 
than  the 
number  of 
synodic 
months. 

The  moon's 
path  on  the 
celestial 
sphere. 


The  nodes. 


Regression 
of  the  nodes. 


Jit  —  JxL 

Another  way  of  looking  at  the  matter,  leading,  of  course,  to  the  same 
result,  is  this  :  In  a  sidereal  year  the  number  of  sidereal  months  must  be 
just  one  greater  than  the  number  of  synodic  months  ;  the  numbers  are, 
respectively,  13.369+  and  12.369  +  . 

192.  The  Moon's  Path  on  the  Celestial  Sphere  ;  the  Nodes  and 
their  Motion.  —  By  observing  the  moon's  right  ascension  and 
declination  daily  with  suitable  instruments  we  can  map  out  its 
apparent  path,  just  as  in  the  case  of  the  sun  (Sec.  156).  It 
turns  out  to  be  (very  nearly)  a  great  circle  inclined  to  the 
ecliptic  at  an  angle  of  about  5°  8',  but  varying  12'  each  way, 
from  4°  56'  to  5°  20'. 

The  two  points  where  the  path  cuts  the  ecliptic  are  called 
the  nodes,  the  ascending  node  being  the  one  where  the  moon 
passes  from  the  south  side  to  the  north  side  of  the  ecliptic. 
The  opposite  node  is  called  the  descending  node.  (Ancient 
astronomers  all  lived  in  the  northern  hemisphere.) 

The  moon  at  the  end  of  the  month  never  comes  back  exactly 
to  the  point  of  beginning,  on  account  of  the  so-called  "  pertur- 
bations," due  to  the  attraction  of  the  sun. 

One  of  the  most  important  of  these  perturbations  is  the 
regression  of  the  nodes.  These  slide  westward  on  the  ecliptic 
in  the  same  manner  as  the  vernal  equinox  does,  but  much 
faster,  completing  their  circuit  in  a  little  less  than  nineteen 


THE  MOON  169 

years  instead  of  twenty-six  thousand.    The  average  time  between 

two  successive  passages  of  the  moon  through  the  same  node  is 

called  the  nodical  or  draconitic  month.     It  is  27.2122  days, —  The  nodical 

an  important  period  in  the  theory  of  eclipses. 

When  the  ascending  node  of  the  moon's  orbit  coincides  with 
the  vernal  equinox  the  angle  between  the  moon's  path  and  the 
equator  has  its  maximum  value  of  23°  27'  4-  5°  8',  or  28°  35';   Variation  in 
nine  and  one-half  years  later,  when  the  descending  node  has  come  *?e  mclma~ 

tion  of  the 

to  the  same  point,  the  angle  is  only  23°  27'  -  5°  8',  or  18°  19'.  mo0n's  path 

In  the  first  case  the  moon's  meridian  altitude  will  range  during  to  the  celes- 
the  month  through  about  57°.     In  the  second  case  the  range  is 
reduced  to  36°  38'. 

193.    Interval  between  the  Moon's  Successive  Transits ;  Daily  interval 

Retardation  of  its  Rising  and  Setting.  —  Owing  to  the  eastward  between 

0  successive 

motion  of  the  moon  it  comes  to  the  meridian  later  each  day.  transits  of 
If  we  call  the  average  interval  between  its  successive  transits  a  themoon,— 

24h50m.5. 

"  moon  day,"  we  see  at  once  that  while  in  the  synodic  month 
there  are  29.5306  mean  solar  days,  there  must  be  just  one  less 
of  these  "  moon  days,"  since  the  moon,  in  the  synodic  month, 
moves  around  eastward  from  the  sun  to  the  sun  again,  thus 
losing  one  complete  relative  rotation. 

It  follows,  therefore,  that  the  length  of  the  "  moon  day"  must 

be  24h  x  — '- ,  or  24h50m.51,   the  average  "  daily  retarda-  How  the 

28.5306  daily  retard- 

tion  "  being  50i  minutes.  It  ranges,  however,  all  the  way  from  ation  is 
38  minutes  to  66  minutes  on  account  of  the  variations  in  the 
rate  of  the  moon's  motion  in  right  ascension,  —  due  partly  to 
perturbation,  but  mainly  to  the  oval  form  of  its  orbit  and  its 
inclination  to  the  celestial  equator,  —  variations  precisely  analo- 
gous to  the  inequalities  of  the  sun's  motion,  which  produce  the 
equation  of  time  (Sec.  174),  but  many  times  greater. 

The  average  retardation  of  the  moon's  daily  rising  and  setting 
is  also  the  same  50.51  minutes,  but  the  actual  retardation  is 
much  more  variable  than  that  of  the  transits,  depending  largely 


170 


MANUAL   OF   ASTRONOMY 


Daily  re- 
tardation 
of  moon's 
rising  and 
setting 
ranges  in 
our  latitude 
from  23m  to 
Ih17m. 

One  day  in 
each  month 
when  the 
moon  does 
not  rise. 


on  the  latitude  of  the  observer.  At  New  York  the  range  is 
from  23  minutes  to  77  minutes.  In  higher  latitudes  it  is  still 
greater.  Indeed,  in  latitudes  above  61°  20',  the  moon,  when 
it  has  its  greatest  possible  declination  of  28°  47',  will  become 
drcumpolar  for  a  certain  time  each  month  and  will  remain  visible 
without  setting  at  all  for  a  whole  day  or  more,  according  to 
the  latitude  of  the  observer.  As  a  consequence  of  this  daily 
retardation  it  follows  that  there  is  always  one  day  in  the  month 
on  which  the  moon  does  not  rise,  and  another  on  which  it  does 
not  set. 

194.  Harvest  and  Hunter's  Moon.  —  The  full  moon  that 
comes  nearest  the  autumnal  equinox  is  known  as  the  harvest- 
moon;  the  one  next  following  is  the  hunter's  moon.  At  that 
time  of  the  year  the  moon  while  nearly  full  rises  for  several 


FIG.  04.  —  Explanation  of  the  Harvest-Moon 

Harvest  and  consecutive  nights  at  about  the  same  hour,  so  tha,t  the  moon- 
light evenings  last  for  an  unusual  length  of  time.  The  phe- 
nomenon is  much  more  striking  in  Northern  Europe  than  in 
the  United  States. 

In  the  autumn  the  full  moon  is  near  the  vernal  equinox 
(since  the  sun  is  at  the  autumnal)  and  is  in  the  portion  of  its 
path  which  is  least  inclined  to  the  eastern  horizon,  where  it 
rises.  This  is  obvious  from  Fig.  64,  which  represents  a  celestial 


THE   MOON  171 

globe  looked  at  from  the  east.     HN  is  the  horizon,  E  the  east 
point,  P  the  pole,  and  EQ  the  equator.     If,  now,  the  first  of  Explanation 
Aries  is  rising  at  E,  the  line  JEJ1  will  be  the  ecliptic  and  will  of  the 
be  inclined  to  the   horizon  at  an  angle  less  than   QEH  (the  f 


inclination  of  the  equator)  by 

If  the  ascending  node  of  the  moon's  orbit  happens  to  coincide 
with  the  first  of  Aries,  then,  when  this  node  is  rising,  the  moon's 
path  will  lie  still  more  nearly  horizontal  than  JJ1,  as  shown  by 
the  line  MM',  and  the  phenomenon  of  the  harvest-moon  will 
be  specially  noticeable. 

195.  Form   of   the  Moon's   Orbit  ---  By  observation   of  the 
moon's  apparent  diameter,  combined  with  observations  of  her  The  moon's 
place  in  the  sky,  we  can  determine  the  form  of  her  orbit  around  °^li;  an  . 
the  earth  in  the  same  way  that  the  form  of  the  earth's  orbit  amean 
around  the  sun  was  worked   out  in  Sec.  160.     The  moon's  eccentricity 
apparent  diameter  ranges  from  33'  33",  when  as  near  as  pos- 

sible, to  29'  24",  when  most  remote. 

The  orbit  turns  out  to  be  an  ellipse  like  that  of  the  earth 
around  the  sun,  but  of  much  greater  eccentricity,  averaging 
about  .i-g.  We  say  "  averaging  "  because  it  varies  from  -^  to 
^Y  on  account  of  perturbations. 

The  point  of  the  moon's  orbit  nearest  the  earth  is  called  the  Definition  of 
perigee  (Trepi  77}),  that  most  remote  the  apogee  (CLTTO  77)),  and  Pensee' 
the  indefinite  line  passing  through  these  points  and  continuing  apsides. 
to  the  heavens  the  line  of  apsides,  the  major  axis  being  that 
portion  of  this  line   which  lies  between  perigee  and  apogee. 
On  account  of  perturbations  the  line  of  apsides  is  in  continual  Eastward 
motion  like  the  line  of  nodes,  but  it  moves  eastward  instead  of  "J0*1011  of 

»  the  line  of 

westward,  completing  its  revolution  in  about  nine  years.  apsides. 

In  her  motion  around  the  earth  the  moon  also  very  nearly 

observes  the  same  "  law  of  areas  "  that  the  earth  does  in  her  Law  of 

orbit  around  the  sun.  moon's  orbi- 

tal  motion. 

196,  Method  of  determining  the  Size  of  the  Moon's  Orbit, 
i.e.,  her  Distance  and  Parallax.  —  In  the  case  of  any  heavenly 


172 


MANUAL   OF   ASTRONOMY 


Determina- 
tion of  the 
moon's  dis- 
tance from 
the  earth. 


Simultane- 
ous merid- 
ian-circle 
observations 
of  the 
moon's 
zenith-dis- 
tance from 
two  stations 
on  the  same 
meridian 
hut  widely 
separated  in 
latitude. 


body  one  of  the  first  and  most  fundamental  inquiries  relates  to 
its  distance ;  until  this  has  been  measured  we  can  get  no  knowl- 
edge of  the  real  dimensions  of  its  orbit,  nor  of  the  size,  mass, 
etc.,  of  the  body  itself.  The  problem  is  usually  solved  by 
measuring  the  " parallactic  displacement"  (Sec.  78)  due  to  a 
known  change  in  the  position  of  the  observer.  Many  methods 
are  applicable  in  the  case  of  the  moon.  We  limit  ourselves  to 

a  single  one,  the  simplest, 
though  perhaps  not  the  most 
accurate,  of  the  different 
methods  that  are  practically 
available. 

At  each  of  two  observa- 
tories, B  and  C  (Fig.  65), 
on,  or  very  nearly  on,  the 
same  meridian  and  very  far 
apart  (Berlin  and  Cape  of 
Good  Hope,  for  instance), 
the  moon's  zenith-distance,  ZBM  and  Z'CM,  is  observed  simul- 
taneously with  the  meridian-circle.  This  gives  in  the  quadri- 
lateral BOCM  the  two  angles  OEM  and  OCM.  The  angle  BOG, 
at  the  center  of  the  earth,  is  the  difference  of  the  geocentric 
latitudes  of  the  two  observatories  (numerically  their  sum). 
Moreover,  the  sides  BO  and  CO  are  known,  being  radii  of  the 
earth. 

The  quadrilateral  can,  therefore,  be  solved  by  a  simple  trigo- 
nometrical process.  (1)  In  the  triangle  BOC  we  have  given  BO, 
OC,  and  the  included  angle  BOC',  hence,  we  can  find  the  side 
BC  and  the  two  angles  OBC  and  OCB.  (2)  In  the  triangle 
BCM  we  now  have  given  BC  and  the  two  angles  MBC  and 
MCB  (which  are  got  by  simply  subtracting  OBC  from  OBM 
and  OCB  from  OCM)  ;  hence,  we  can  find  BM  and  CM.  (3)  In 
the  triangle  OB M  or  OCM  we  now  know  the  two  sides  and 
the  included  angle  at  B  or  C,  from  which  we  can  find  OM,  the 


FIG.  65.  — Determination  of  the  Moon's 
Parallax 


THE   MOON  173 

moon1  s  distance  from  the  center  of  the  earth.  (4)  When  OM  is 
determined  we  at  once  find  the  horizontal  parallax  from  the 
equation  nrt 


197.  Parallax,  Distance,  and  Velocity  of  the  Moon  --  The 

moon's  equatorial  horizontal  parallax  is  found  to  average  3422".0  Mean  par- 
(57'  2".0),  according  to  Neison,  but  it  varies  considerably  from  allax  of 
day  to  day  on  account  of  the  eccentricity  of  the  orbit.     Her  57'  02". 
average  distance  from  the  earth  is  about  60.3  times  the  earth's  Distance 
equatorial   radius,   or   238840   miles,   with    an    uncertainty  of  miles 
10  or  20  miles. 

The  maximum  and  minimum  values  of  the  moon's  distance  Range  of 
are  mven  by  Neison  as  252972  and  221614  miles.     It  will  be  distance 

*  about  31400 

noted  that  the  "  average     distance  is  not  the  mean  of  the  two  miles. 
extremes. 

Knowing  the  size  and  form  of  the  moon's  orbit,  the  velocity  The  moon's 
of  her  motion  is  easily  computed.     It  averages  2287  miles  an  orbltal 
hour,  or  about  3350  feet  per  second.     Her  mean  angular  velocity 
in  the  celestial  sphere  is  about  33'  an  hour,  just  a  little  greater 
than  the  apparent  diameter  of  the  moon  itself. 

198,  Form  of  the  Moon's  Orbit  with  Reference  to  the  Sun.  — 
While  the  moon  moves  in  a  small  oval  orbit  around  the  earth, 
it  also  moves  around  the  sun  in  company  with  the  earth.     This 
common   motion  of  the  moon  and  earth,  of  course,  does  not 
affect  their  relative  motion,  but  to  an  observer  outside  the  sys- 
tem  looking  down  upon  moon  and  earth  the  moon's  motion 
around  the  earth  would  be  a  very  small  component  of  the  moon's 
whole  motion  as  seen  by  him. 

The  distance  of  the  moon  from  the  earth  is  only  about  -%\-§  The  moon's 
part  of  the  distance  of  the  sun.     The  speed  of  the  earth  in  its  Pathreiative 

r  <  r  to  the  sun 

orbit  around  the  sun  is  also  more  than  thirty  times  greater  than  always  con- 
that  of  the  moon  around  the  earth  ;  for  the  moon,  therefore,  cave  towards 
the  resulting  path  in  space  is  one  which  deviates  very  slightly 


174 


MANUAL   OF   ASTRONOMY 


from  the  orbit  of  the  earth  and  is  always  concave  towards  the  sun, 
as  shown  in  Fig.  66.  It  is  not  as  shown  in  Figs.  67  and  68, 
although  often  so  represented. 

If  we  represent  the  orbit  of  the  earth  by  a  circle  with  a  radius  of 
100  inches  (8  feet  4  inches),  the  moon  would  deviate  from  it  by  only 
one  fourth  of  an  inch  on  each  side,  crossing  it  twenty-four  or  twenty-five 
times  in  one  revolution  around  the  sun,  i.e.,  in  a  year. 

199.   Diameter,  Area,  and  Volume,  or  Bulk,  of  the  Moon.  - 
The  mean  apparent  diameter  of  the  moon  is  31'  1".     Knowing 


3rd  Quarter 


FuU 


New 


1st  Quarter 


FIG.  66.  —  Moon's  Path  Relative  to  the  Sun 


FIG.  67 


FIG.  68 


Erroneous  Representation  of  the  Moon's  Path 

its  mean  distance,  we  easily  compute  from  this  (Sec.  10)  its  real 
diameter,  2163  miles.     This  is  0.273  of  the  earth's  diameter,— 
somewhat  more  than  one  quarter. 

Since  the  surfaces  of  globes  vary  as  the  squares  of  their 
diameters,  and  their  volumes  as  the  cubes,  this  makes  the  sur- 
face area  of  the  moon  equal  to  0.0747  (about  T\)  of  the  earth's, 
and  the  volume,  or  bulk,  0.0204  (almost  exactly  ^)  of  the 
earth's. 

No  other  satellite  is  nearly  as  large  as  the  moon  in  compari- 
son with  its  primary  planet.  The  earth  and  moon  together,  as 
seen  from  a  distance,  are  really  in  many  respects  more  like  a 
double  planet  than  a  planet  and  satellite  of  ordinary  proportions, 


THE  MOON  175 

When  Venus  happens  to  be  nearest  us  (at  a  distance  of  about  twenty-  Earth  and 
five  millions  of  miles)  her  inhabitants,  if  she  has  any,  see  the  earth  about   moon  as 
twice  as  brilliant  as  Yenus  herself  at  her  best  appears  to  us,  and  the   seen  from 
moon,  about  as  bright  as  Sirius,  oscillating  backwards  and  forwards  about 
half  a  degree  on  each  side  of  the  earth. 

200.   Mass,  Density,  and  Superficial  Gravity  of  the  Moon.  - 

The  accurate  determination  of  the  moon's  mass  is  practically  a  Determina- 
difficult  problem.     Though  she  is  the  nearest  of  all  the  heavenly 
bodies,  it  is  far  more  difficult  to  weigh  her  than  to  determine  the  moon, 
mass  of  Neptune,  the  remotest  of  the  planets.     There  are  many 
different  methods  of  dealing  with  the  problem. 

One,  perhaps  the  best,  consists  in  determining  the  position 
of  the  center  of  gravity,  or  center  of  mass,  of  earth  and  moon. 
It  is  this  point  and  not  the  earth's  center  which  describes 
around  the  sun  what  is  called  the  "  orbit  of  the  earth."  Now 
the  earth  and  moon  revolve  together  around  this  common  center 
of  gravity  every  month  in  orbits  exactly  alike  in  form,  but 
differing  greatly  in  size,  the  earth's  orbit  being  as  much  smaller 
than  the  moon's  as  its  mass  is  greater. 

On  account  of  this  monthly  motion  of  the  earth's  center,  there 
results  necessarily  a  "lunar  equation,"  i.e.,  a  slight  alternate  The  "lunar 
eastward  and  westward  displacement  in  the  heavens  of  every  f<iu^tlon" 

J     in  the  appar- 

object  viewed  from  the  earth  as  compared  with  the  place  the  ent  motion 
object  would  occupy  if  the   earth  had  no  such  motion.     In  of  the  sun 

and  nearer 

the  case  of  the  stars  or  the  remoter  planets  the  displacement  pianets. 
is  not  sensible ;  but  it  can  be  measured  by  observing  through 
the  month  the  apparent  motion  of  the  sun,  or  better,  of  one  of 
the  nearer  planets,  as  Mars  or  Venus,  or  the  newly  discovered 
Eros. 

From  such  observations  it  is  found  that  the  radius  of  the 
monthly  orbit  of  the  earth's  center  (i.e.,  the  distance  from  the 
earth's  center  to  the  common  center  of  gravity  of  earth  and  moon) 

is  2880  miles.     This  is  just  about  — — -  of  the  distance  from  the 


176 


MANUAL   OF   ASTRONOMY 


The  moon's    earth  to  the  moon,  whence  we  conclude  that  the  mass  of  the 

that  of  the  earth. 


mass  is  jYTs 

the  mass  of     moon  IS 

the  earth. 


81.5 


Density  of 
the  moon 
about  three 
fifths  the 
density  of 
the  earth. 


Gravity  on 
the  moon's 
surface 
about  one 
sixth  of 
gravity  on 
the  earth ; 
important  in 
relation  to 
the  constitu- 
tion of  the 
moon. 

Rotation  of 
the  moon  on 
its  axis.    The 
period  of  ro- 
tation equals 
the  sidereal 
month. 


For  other  methods  of  determining  the  mass  of  the  moon,  the  reader  is 
referred  to  the  General  Astronomy,  Art.  243. 

201,  Since  the  density  of  a  body  is  equal  to  its  mass  -f-  volume, 

the  density  of  the  moon  compared  with  the  earth  is  — — •  divided 
-j  81.5 

by  — ,  which  equals  0.601,  or  about  3.4  the  density  of  water,  the 

earth's  density  being  5.53.  This  is  a  little  above  the  average 
density  of  the  rocks  which  compose  the  crust  of  the  earth.  This 
low  density  of  the  moon  is  not  at  all  surprising,  nor  at  all  incon- 
sistent with  the  belief  that  it  once  formed  a  part  of  the  earth, 
since,  if  such  were  the  case,  the  moon  was  probably  formed  by 
the  separation  of  the  outer  portions  of  that  mass,  which  would 
be  likely  to  be  lighter  than  the  rest. 

The  superficial  gravity,  or  the  attraction  of  the   moon  for 

bodies  at  its  surface,  is  mass  -*-  radius2,  i.e.,  — —  divided  by-0.2732, 

81.5 

and  comes  out  about  one  sixth  of  gravity  at  the  surface  of  the 
earth.  That  is,  a  body  weighing  six  pounds  on  the  earth's  sur- 
face would,  at  the  surface  of  the  moon,  weigh  only  one  pound 
(by  a  spring-balance).  A  man  who  can  leap  to  a  height  of  5  feet 
here  would  reach  30  fest  there,  and  so  on.1 

This  is  a  point  that  must  be  borne  in  mind  in  connection 
with  the  enormous  scale  of  the  surface  structure  of  the  moon. 
Volcanic  forces  on  the  moon  would  throw  ejected  materials  to 
a  vastly  greater  distance  than  on  the  earth. 

202.  Rotation  of  the  Moon.  —  The  moon  rotates  on  its  axis 
once  a  sidereal  month,  in  exactly  the  same  time  as  that  occupied 
by  its  revolution  around  the  earth;  its  day  and  night,  therefore, 
the  interval  between  sunrise   and  sunset,   are  each  nearly  a 

1  But  see  Sec.  141  for  Professor  Newcomb's  illustration. 


THE   MOON  177 

fortnight  in  length,  and  in  the  long  run  it  keeps  the  same  side 
always  towards  the  earth.  We  see  to-day  precisely  the  same 
aspect  of  the  moon  as  Galileo  did  in  the  days  when  he  first 
turned  his  telescope  upon  it. 

Many  find  difficulty  in  seeing  why  a  motion  of  this  sort  should  be 
called  a  "  rotation  "  of  the  moon,  since  it  is  extremely  like  the  motion  of  a 
ball  carried  on  a  revolving  crank  (Fig.  69).  "  Such  ^— -^ 

a  ball,"  they  say,  "revolves  around  the  shaft,  but       r*-*-] (       ) 

does  not  rotate  on  its  own  axis."  It  does  rotate, 
however ;  for  if  we  mark  one  side  of  the  ball,  we 
shall  find  the  marked  side  presented  successively  to 
every  point  of -the  compass  as  the  crank  turns,  so  that 
the  ball  turns  on  its  own  axis  as  really  as  if  it  were 
whirling  upon  a  pin  fastened  to  the  table. 

By  virtue  of  its  connection  with  the  crank,       U 
the  ball  has   two  distinct  motions:    (1)  the 
motion  of  translation,  which  carries  its  center  in  a  circle  around 
the  axis  of  the  shaft;  (2)  an  additional  motion  of  rotation1  around  Rotation 
a  line  drawn  through  its  center  parallel  to  the  shaft.     The  pin  A  of  a.ba11 
(in  the  figure)  and  the  hole  in  which  it  fits  both  rotate  at  the  crank  arm.  * 
same  rate,  so  that  the  ball,  while  it  turns  on  its  "  axis  "  (an 
imaginary  line),  does  not  turn  on  the  pin,  nor  the  pin  in  the  hole. 

203,   Librations.  —  While  in  the  "  long  run  "  the  moon  keeps  The  rotation 
the  same  face  towards  the  earth,  it  is  not  so  in  the  short  run;  of  themoon 

.  .  ,  independent 

there  is  no  crank  connection  between  the  earth  and  moon,  and  Of  its  orbital 
the  moon  in  different  parts  of  a  single  month  does  not  keep  revolution 
exactly  the  same  face  towards  the  earth,  but  rotates  with  per-  having  the 
feet  independence  of  her  orbital  motion.      With  reference  to  same  period, 
the  center  of  the  earth  the  moon's  face  is  continually  oscillating 
slightly,  and  these  oscillations  constitute  what  are  called  libra- 
tions,  of   which  we   distinguish  three,  —  viz.,  the  libration  in 
latitude,  the  libration  in  longitude,  and  the  diurnal  libration. 

1  Rotation  consists  essentially  in  this  :  that  a  line  connecting  any  two  points, 
and  not  parallel  to  the  axis  of  the  rotating  body,  will  sweep  out  a  circle  on  the 
celestial  sphere,  if  produced  to  it. 


178 


MANUAL   OF   ASTRONOMY 


Inclination 
of  the 
moon's 
equator  to 
the  plane  of 
her  orbit, 
causing 
libration  in 
latitude. 


Rotation 
uniform, 
while  orbital 
motion  is 
variable, 
causing 
libration  in 
longitude. 

Apparent 
libration 
due  to 
observer's 
displace- 
ment by  the 
rotation  of 
the  earth. 


Minute 

physical 

libration. 


Coincidence 
of  periods  of 
rotation  and 
orbital  revo- 
lution prob- 
ably to  be 
explained 
by  tidal 
evolution. 


(1)  The  libration  in  latitude  is  due  to  the  fact  that  the  moon's 
equator  does  not  coincide  with  the  plane  of  its  orbit,  but  makes 
with  it  an  angle  of  about  6£°.     This  inclination  of  the  moon's 
equator  causes  its  north  pole  at  one  time  in  the  month  to  be 
tipped  6 j-°  towards  the  earth,  while  a  fortnight  later  the  south 
pole  is  similarly  inclined  to  us;   just  as  the  north  and  south 
poles  of  the  earth  are  alternately  presented  to  the  sun,  causing 
the  seasons. 

(2)  The  libration  in  longitude  depends  on  the  fact  that  the 
moon's  angular  motion  in  its  oval  orbit  is  variable,  while  the 
motion  of  rotation  is  uniform^  like  that  of  any  other  undis- 
turbed body;   the   two  motions,  therefore,  do  not  keep  pace 
exactly  during  the  month,  and  we  see  alternately  a  few  degrees 
around  the  eastern  and  western  edge  of  the  lunar  globe.     This 
libration  amounts  to  about  7f°. 

(3)  The  diurnal  libration.     Again,  when  the  moon  is  rising 
we  look  over  its  upper,  which  is  then  its  western,  edge,  seeing  a 
little  more  of  that  part  of  the  moon  than  if  we  were  observing 
it  from  the  center  of  the  earth ;  and  vice-  versa  when  it  is  setting. 
This  constitutes  the  so-called  diurnal  libration,  and  amounts  to 
about  one  degree.     Strictly  speaking,  this  diurnal  libration  is  not 
a  libration  of  the  moon,  but  of  the  observer.     The  telescopic 
effect  is  the  same,  however,  as  that  of  a  true  libration. 

In  addition  to  this  there  is  also  a  very  slight  physical 
libration  of  the  moon.  It  is  probable  that  the  diameter  of 
the  moon  directed  towards  the  earth  is  a  little  longer  than  the 
diameter  at  right  angles,  the  difference  being  perhaps  a  few 
hundred  feet ;  and  as  the  moon  revolves  around  the  earth  this 
longest  diameter  oscillates  slightly  from  side  to  side,  changing 
its  position  apparently  about  1£  miles  on  the  moon's  disk. 

The  exact,  long-run  agreement  between  the  moon's  time  of 
rotation  and  of  her  orbital  revolution  cannot  be  accidental.  It 
has  probably  been  caused  by  the  action  of  the  earth  on  some 


THE   MOON 


179 


protuberance  on  the  moon's  surface,  analogous  to  a  tidal  wave. 
If  the  moon  were  ever  plastic,  the  earth's  attraction  must 
necessarily  have  been  to  produce  a  huge  tidal  bulge  upon  her 
surface,  and  the  effect  would  have  been  ultimately  to  force  an 
agreement  between  the  lunar  day  and  the  sidereal  month.  The 
subject  will  be  resumed  later  in  connection  with  tidal  evolution 
(Sec.  346). 

204.   The  Phases  of  the  Moon.  —  Since  the  moon  is  an  opaque 
body  shining  merely  by  reflected  light,  we  can  see  only  that 


Phases  of 
the  moon 
due  to  the 
fact  that  we 
see  only  a 
varying  por- 
tion of  her 
illuminated 
hemisphere, 


FIG.  70.  —  Explanation  of  the  Moon's  Phases 

hemisphere  of  her  surface  which  happens  to  be  illuminated, 
and  of  this  hemisphere  only  that  portion  which  happens  to  be 
turned  towards  the  earth.  When  the  moon  is  between  the 


180 


MANUAL   OF   ASTRONOMY 


The  termi- 
nator 
always  a 
semi-ellipse. 


Direction  of 
the  horns  of 
the  crescent 
always 
away  from 
the  sun. 


earth  and  the  sun  (at  new  moon)  the  dark  side  is  then  pre- 
sented directly  towards  us,  and  the  moon  is  entirely  invisible. 
A  week  later,  at  the  end  of  the  first  quarter,  half  of  the  illumi- 
nated hemisphere  is  visible,  just  as  it  is  a  week  after  the  full. 
Between  the  new  moon  and  the  half-moon,  during  the  first 
and  last  quarters  of  the  lunation,  we  see  less  than  half  of 
the  illuminated  portion  and  then  have  the  "crescent"  phase. 
Between  half-moon  and  the  full  moon,  during  the  second  and 
third  quarters  of  the  lunation,  we  see  more  than  half  of  the 
moon's  illuminated  side  and  have  then  what  is  called  the 
"  gibbous  "  phase. 

Fig.  70  (in  which  the  light  is  supposed  to  come  from  a 
point  far  above  the  circle  which  represents  the  moon's  orbit) 
shows  how  the  phases  are  distributed  through  the  month. 

205.  The  Terminator.  —  The  line  which  separates  the  dark 
portion  of  the  disk  from  the  bright  is  called  the  terminator  and 
is  always  a  semi-ellipse,  since  it  is  a  semicircle  viewed  obliquely. 
The  illuminated  portion  of  the  moon's  disk  is,  therefore,  always 
a  figure  which  is  made  up  of  a  semicircle  plus  or  minus  a  semi- 
ellipse,  as  shown  in  Fig.  71  A.  At  new 
or  full  moon,  however,  the  semi-ellipse 
becomes  a  semicircle.  It  is  sometimes 
incorrectly  attempted  to  represent  the 
crescent  form  by  a  construction  like 
Fig.  71  B,  in  which  a  smaller  circle  has 
a  portion  cut  out  of  it  by  an  arc  of  a  larger  one. 

It  is  to  be  noticed  also  that  db,  the  line  which  joins  the 
"  cusps,"  or  points  of  the  crescent,  is  always  perpendicular  to 
a  line  drawn  from  the  moon  to  the  sun,  so  that  the  horns  are 
always  turned  away  from  the  sun.  The  precise  position,  there- 
fore, in  which  they  will  stand  at  any  time  is  perfectly  predict- 
able and  has  nothing  whatever  to  do  with  the  weather.  Artists 
are  sometimes  careless  in  representing  a  crescent  moon  with  its 
horns  pointed  downwards,  which  is  impossible. 


FIG.  71 


THE   MOON  181 

206.  Earth-Shine    on  the    Moon.  —  Near   the   time   of    new 
moon  the  whole  disk  is  easily  visible,  the  portion  on  which 
sunlight  does  not  fall  being  illuminated  by  a  pale  reddish  light. 

This  light  is  earth-shine,  the  earth  as  seen  from  the  moon  being  Earth-shine 
then  nearly  "  full."  on  the moon- 

Seeij  from  the  moon,  the  earth  would  show  all  the  phases  that 
the  moon  does,  the  earth's  phase  being  in  every  case  exactly 
supplementary  to  that  of  the  moon  as  seen  by  us  at  the  time. 
Taking  everything  into  account,  the  earth-shine  by  which  the 
moon  is  illuminated  near  new  moon  is  probably  from  fifteen  to 
twenty  times  as  strong  as  the  light  of  the  full  moon.  The 
ruddy  color  is  due  to  the  fact  that  the  light  sent  to  the  moon 
from  the  earth  has  passed  twice  through  our  atmosphere  and 
so  has  acquired  the  sunset  tinge. 

PHYSICAL   CHAKACTEKISTICS    OF   THE   MOON 

207.  The  Moon's  Atmosphere The  moon's  atmosphere,  if  No  sensible 

any  exists,   is  extremely  rare,  probably  not  producing  at  the 
moon's  surface  a  barometric  pressure  to  exceed  -£%  of  an  inch 

of  mercury,  or  y^  of  the  atmospheric  pressure  at  the  earth's 
surface.     The   evidence   on   this   point  is  twofold. 

First,  the  telescopic  appearance.     The  parts  of  the  moon  near  No  haze,  all 
the  edge  of  the  disk,  or  "  limb,"  which,  if  there  were  any  atmos-  s^^s 
phere,  would  be  seen  through  its  greatest  possible  depth,  are  black;  no 
visible  without  the  least  distortion.     There  is  no  haze,  and  all  cloudsor 

atmospheric 

the  shadows  are  perfectly  black ;  there  is  no  evidence  of  clouds  phenomena. 
or  storms,  or  of  anything  like  the  ordinary  phenomena  of  the 
terrestrial  atmosphere. 

Second,  the  absence  of  refraction  at  the  moon's  limb,  when  the  No  sensible 

moon  intervenes  between  us  and  any  more  distant  object.     At  an  refrac^onof 

eclipse  of  the  sun  there  is  no  distortion  of  the  sun's  limb  where  which  pass 

the  moon  cuts  it.     When  the  moon  "  occults  "  a  star  there  is  close  to  the 

,.  i  i       T       i        moon's  limb. 

no  distortion  or  discoloration  of  the   star  disk,  but  both  the 


182 


MANUAL   OF   ASTRONOMY 


No  water  on 
the  moon. 


How  came 
the  moon  to 
lose  her 
atmos- 
phere ? 


Partly,  per- 
haps, by 
absorption, 
occlusion, 
and  chem- 
ical combi- 
nation in 
rocks. 


Perhaps  by 
flight. 


disappearance  and  reappearance  are  practically  instantaneous. 
Moreover,  an  atmosphere  of  even  slight  density,  quite  insuffi- 
cient to  produce  any  sensible  distortion  of  the  image,  would 
notably  diminish  the  time  during  which  the  star  would  be  con- 
cealed behind  the  moon,  since  the  refraction  would  bend  the 
rays  from  the  star  around  the  edge  of  the  moon  so  as  to  render 
it  visible,  both  after  it  had  really  passed  behind  the  limb  and 
before  it  emerged  from  it.  There  are  some  rather  doubtful 
indications  of  a  very  slight  effect  of  this  kind,  corresponding 
to  what  would  be  produced  by  an  atmosphere  about  j^Vo  as 
dense  as  our  own. 

208.  Water  on  the  Moon's  Surface Of  course,  if  there  is 

no  atmosphere  there  can  be  no  liquid  water,  since  if  there  were 
it  would  immediately   evaporate  and  form  an  atmosphere  of 
vapor.     It  is  not  impossible,  however,  nor  perhaps  improbable, 
that  solid  water,  i.e.,  ice  and  snow,  may  exist  on  parts  of  the 
moon's    surface   at  a   temperature   too  low   to   liberate   vapor 
enough  to  make  an  atmosphere  observable  from  the  earth. 

209,  What  has  become  of  the  Moon's  Air  and  Water?  —  If 
the  moon  ever  formed  a  part  of  the  same  mass  as  the  earth, 
she  must  once  have  had  both  air  and  water.     There  are  a  num- 
ber of  possible,  and  more  or  less  probable,  hypotheses  to  account 
for  their  disappearance :   (1)  The  air  and  water  may  have  struck 
in,  —  partly  absorbed  by  porous  rocks  and  partly  disposed  of  in 
cavities  left  by  volcanic  action ;  partly  also,  perhaps,  by  chemi- 
cal combination  as  water  of  crystallization,  and  by  simple  occlu- 
sion.    (2)  The  atmosphere  may  have  flown  away ;  and  this  is 
perhaps  the  most  probable  hypothesis,  though  it  is  quite  possible 
that  this  cause  and  the  preceding  may  have  cooperated.     If  the 
"  kinetic  "  theory  of  gases  is  true,  no  body  of  small  mass,  not 
extremely  cold,  can  permanently  retain  any  considerable  atmos- 
phere.    A  particle  leaving  the  moon  with  a  speed  exceeding 
the   "  critical    velocity "   of   1£   miles    a   second   would  never 
return  (Sec.  319).     If  she  was  ever  warm,  the  molecules  of  her 


THE  MOON  183 

atmosphere  must  have  been  continually  acquiring  velocities 
greater  than  this,  and  deserting  her  one  by  one.  (See  Physics, 
pp.  231,  232.) 

However  it  came  about,  it  is  quite  certain  that  at  present  no 
substances  that  are  gaseous  or  vaporous  at  low  temperatures 
exist  in  any  considerable  quantity  on  the  moon's  surface,  —  at 
least,  not  on  our  side  of  it. 

210.   The  Moon's  Light.  —  As  to  quality,  it  is  simply  sunlight,  Light  of  the 
showing  a  spectrum  identical  in  every  detail  with  that  of  light  m^^   In 
coming  directly  from  the  sun  itself;   and  this  may  be  noted  identical 
incidentally  as  an  evidence  of  the  absence  of  a  lunar  atmosphere,  ^lth  sun" 
which,  if  it  existed  in  any  quantity,  would  produce  markings  of 
its  own  in  the  spectrum. 

The  brightness  of  full  moonlight  as  compared  with  sunlight 
is  estimated  as  about  ^^Voir  •     According  to  this,  if  the  whole  Light  of  full 
visible   hemisphere  were  packed  with  full  moons,  we  should  m°onabout 
receive  from  it  about  one-eighth  part  of  the  light  of  the  sun.       sunlight. 

Moonlight  is  not  easy  to  measure,  and  different  experimenters  have 
found  results  for  the  ratio  between  the  light  of  the  full  moon  and  sunlight 
ranging  all  the  way  from  -^Viro  (Bouguer)  to  ^^TTTT  (Wollaston).  The 
value  now  generally  accepted  is  that  determined  by  Zollner,  viz.,  ^^fo^ . 

The  half-moon  does  not  give,  even  approximately,  half  as  Sudden 
much  light  as  the  full  moon.     Near  the  full  the  brightness  increaseof 

brightness 

suddenly  and  greatly  increases,  probably  because  at  any  time  near  full 
except  at  the  full  moon  the  moon's  visible  surface  is  more  or  moon, 
less  darkened  by  shadows. 

The  average  albedo,  or  reflecting  power  of  the  moon's  surface,  Moon  re- 
Zollner  states  as  0.174;  i.e.,  the  moon's  surface  reflects  a  little  fleet*  about 

one  sixth  of 

more  than  one-sixth  part  of  the  light  that  falls  upon  it.  the  light 

This  corresponds  to  the  reflecting  power  of  a  rather  light-  whichit 
colored  sandstone.     There   are,  however,  great  differences  in 
the  brightness  of  the  different  portions  of  the  moon's  surface. 
Some  spots  are  nearly  as  white  as  snow  or  salt,  and  others  as 
dark  as  slate. 


184 


MANUAL   OF   ASTRONOMY 


Heat  re- 
ceived from 
the  full 
moon  prob- 
ably about 
iKoW  of  that 
received 
from  the 
sun. 


Mainly 
obscure 
heat. 


Mean  tem- 
perature of 
the  moon 
extremely 
low,  but 
range  of 
temperature 
probably 
very  great. 


Oscillations 
of  opinion. 


211.  Heat  of  the  Moon.  —  For  a  long  time  it  was  impossible 
to  detect  the  moon's  heat  by  observation.     Even  when  concen- 
trated by  a  large  lens,  it  is  too  feeble  to  be  shown  by  the  most 
delicate  thermometer.     The  first  sensible  evidence  of   it  was 
obtained  by  Melloni  in  1846,  with  the  newly  invented  thermo- 
pile, by  a  series  of  observations  from  the  summit  of  Vesuvius. 

With  modern  apparatus  it  is  easy  enough  to  perceive  the 
heat  of  lunar  radiation,  but  the  measurements  are  extremely 
difficult. 

A  considerable  percentage  of  the  lunar  heat  seems  to  be  heat 
simply  reflected  like  light,  while  the  rest,  perhaps  three  quarters 
of  the  whole,  is  "  obscure  heat,"  i.e.,  heat  which  has  first  been 
absorbed  by  the  moon's  surface  and  then  radiated,  like  the  heat 
from  a  brick  surface  that  has  been  warmed  by  sunshine.  This 
is  shown  by  the  fact  that  a  comparatively  thin  plate  of  glass 
cuts  off  some  eighty-six  per  cent  of  the  moon's  heat. 

The  total  amount  of  heat  radiated  by  the  full  moon  to  the 
earth  is  estimated  by  Lord  Rosse  at  about  one  eighty -thousandth 
part  of  that  sent  us  by  the  sun ;  but  this  estimate  is  probably 
too  high.  Prof.  0.  C.  Hutchins  in  1888  found  it  T^VTnr 

212.  Temperature  of  the  Moon's  Surface.  —  As  to  the  tempera- 
ture of  the  moon's  surface,  it  is  difficult  to  affirm  much  with 
certainty.     On  the  one  hand,  the  lunar  rocks  are  exposed  to  the 
sun's  rays  in  a  cloudless  sky  for  fourteen  days  at  a  time,  so 
that  if  they  were  protected  by  air  like  the  rocks  upon  the  earth 
they  would  certainly  become    intensely  heated.     During   the 
long  lunar  night  of  fourteen  days  the  temperature  must  inevi- 
tably fall  appallingly  low,  perhaps  200°  below  zero. 

There  have  been  great  oscillations  of  opinion  on  this  subject. 
Some  years  ago  Lord  Rosse  inferred  from  his  observations  that 
the  maximum  temperature  attained  by  the  moon's  surface  was 
not  much,  if  at  all,  below  that  of  boiling  water ;  but  his  own 
later  investigations  and  those  of  Langley  threw  great  doubt 
on  this  conclusion,  rather  indicating  that  the  temperature  never 


THE   MOON  185 

reaches  that  of  melting  ice.  The  latest  observations,  however  — 
the  elaborate  work  of  Very  in  1899  —  corroborate  Lord  Rosse's 
earlier  results  and  show  almost  conclusively  that  on  the  moon's 
equator  at  lunar  noon  the  temperature  rises  very  high,  falling 
correspondingly  low  when  night  comes  on. 

Lord  Rosse  has  also  found  that  during  a  total  eclipse  of  the  Sudden  dis- 
moon  her  heat  radiation  practically  vanishes  and  does  not  regain  aPPearance 
its  normal  value  until  some  hours  after  she  has  left  the  earth's  heat  when 
shadow.     This  seems  to  indicate  that  she  loses  heat  nearly  as  immersed  in 

-....,  the  earth's 

last  as  it  is  received.  shadow. 

213.  Lunar  Influences  on  the  Earth.  —  The  moon's  attraction 
cooperates  with  that  of  the  sun  in  producing  the  tides,  to  be 
considered  later. 

There  are  also  certain  distinctly  ascertained  disturbances  of  influences 
terrestrial  magnetism  connected  with  the  approach  and  recession  of  the  moon 

^r  on  the  earth: 

of  the  moon  at  perigee  and  apogee ;  and  this  ends  the  chapter  only  tidal 
of  ascertained  lunar  influences.  action  and  a 

The  multitude  of  current  beliefs  as  to  the  controlling  influ-  ^agnetfc 
ence  of  the  moon's  phases  and  changes  upon  the  weather  and  disturbance, 
the  various  conditions  of  life  are  simply  superstitions,  mostly  Numerous 
unfounded  or  at  least  unverified.  supersti- 

It  is  quite  certain  that  if  the  moon  has  any  influence  at  all  of  which  no 
the  sort  imagined  it  is  extremely  slight,  so  slight  that  it  has  not  evidence  can 
yet  been  demonstrated,  though  numerous  investigations  have 
been  made  expressly  for  the  purpose  of  detecting  it.     It  is  not 
certain,  for  instance,  whether  it  is  warmer  or  not,  or  less  cloudy 
or  not,  at  the  time  of  full  moon. 

214,  The  Moon's  Telescopic  Appearance  and  Surface. — Even 
to  the  naked  eye  the  moon  is  a  beautiful  object,  diversified  with 
markings  which  are  associated  with  numerous  popular  myths. 
In  a  powerful  telescope  these  markings  mostly  vanish  and  are 
replaced  by  a  multitude   of  smaller  details  which  make  the  The  moon  as 
moon,  on  the   whole,   the  finest   of   all  telescopic   objects,  —  a  telesc°Pic 
especially  so  for  instruments  of  a  moderate  size  (say  from  6  to 


186 


MANUAL   OF   ASTRONOMY 


Best  time 
to  look  at 

the  moon. 


broken  by 
afewmoun- 

and  numer- 
ous  craters, 


Dimensions 
of  craters. 


10  inches  in  diameter),  which  generally  give  a  more  pleasing 
view  of  our  satellite  than  instruments  either  much  larger  or 
much  smaller. 

An  instrument  of  this  size,  with  magnifying  powers  between 
250  and  500,  brings  the  moon  optically  within  a  distance  rang- 
ing from  1000  to  500  miles  ;  and  since  an  object  half  a  mile  in 
diameter  on  the  moon  subtends  an  angle  of  about  0".43,  it 
would  be  distinctly  visible.  A  long  line,  or  streak,  even  less 
than  a  quarter  of  a  mile  across  can  probably  be  seen.  With 
larger  telescopes  the  power  can  now  and  then  be  carried  very 
much  higher,  and  correspondingly  smaller  details  made  out,  when 
the  seeing  is  at  its  best,  not  otherwise.  The  right-hand  illustration 
opposite  gives  an  excellent  idea  of  the  moon's  appearance  with 
a  moderate  magnifying  power  of  about  100. 

For  most  purposes  the  best  time  to  look  at  the  moon  is  when 
•{.  -g  between  six  and  ten  days  old.  At  the  time  of  full  moon 
few  objects  on  the  surface  are  well  seen,  as  there  are  then  no 
shadows  to  give  relief. 

It  is  evident  that  while  with  the  telescope  we  should  be  able 
to  see  such  objects  as  lakes,  rivers,  forests,  and  great  cities,  if 
they  existed  on  the  moon,  it  would  be  hopeless  to  expect 
to  distinguish  any  of  the  minor  indications  of  life,  such  as 
buildings  or  roads. 

215,  The  Moon's  Surface  Structure.  —  The  moon's  surface  for 
^e  most  Part  *S  extremely  broken.  With  us  the  mountains  are 
mostly  in  long  ranges,  like  the  Andes  and  Himalayas.  On  the 
moon  the  ranges  are  few  in  number;  but,  on  the  other  hand, 
^e  surface  is  pitted  all  over  with  great  craters,  which  resemble 
very  closely  the  volcanic  craters  on  the  earth's  surface,  though 
on  an  immensely  greater  scale.  The  largest  terrestrial  craters 
do  not  exceed  6  or  7  miles  in  diameter;  many  of  those  on  the 
mOon  are  50  or  60  miles  across,  and  some  have  a  diameter  of 
more  than  100  miles,  while  smaller  ones  from  5  to  20  miles  in 
diameter  are  counted  by  the  hundred. 


188 


MANUAL   OF   ASTRONOMY 


FIG.  72.  —  Normal  Lunar  Crater 


The  normal        The  normal  lunar  crater  (Fig.  72)  is   nearly  circular,  sur- 
lunar  crater.  rOunded  by  a  ring  of  mountains  which  rise  anywhere  from  1000 

to  20000  feet  above 
the  surrounding 
country.  The  floor 
within  the  ring  may 
be  either  above  or 
below  the  outside 
level ;  some  craters 
are  deep,  and  some 
filled  nearly  to  the 
brim.  In  a  few  cases 
the  surrounding 
mountain  ring  is  en- 
tirely absent,  and  the  crater  is  a  mere  hole  in  the  plain. 
Frequently  in  the  center 
of  the  crater  there  rises 
a  group  of  peaks,  which 
attain  about  the  same  ele- 
vation as  the  encircling 
ring,  and  these  central 
peaks  sometimes  show 
holes  or  craters  in  their 
summits.  Fig.  73  is  from 
a  drawing  by  Nasmyth  of 
Gassendi.  the  crater  Gassendi,  which 
is  on  the  southeast  quad- 
rant of  the  moon's  sur- 
face, and  comes  into  view 
about  three  or  four  days 
before  full  moon.  It  is 
58  miles  in  diameter  and 
about  8000  feet  deep. 
Fig.  74  is  also  from  one  of  Nasmyth's  drawings  and  is  a  fine 


FIG.  73.  —  Gassendi 


THE   MOON 


189 


representation  of  Copernicus,  a  crater  not  quite  so  large  or  deep 
as  Gassendi,  but  very  interesting  on  account  of  the  number  of 
surrounding  ridges  and  the  manner  in  which  the  neighboring 
region  is  thickly  sown  with  craterlets  and  holes.  It  is  on  the 
terminator  a  day  or  two  after  the  half -moon. 

In  the  enlarged  photograph  of  a  portion  of  the  moon's 
surface  on  page  187  the  great  crater  at  the  left  is  Theophilus, 
64  miles  in  diameter  and 
nearly  19000  feet  deep. 

On  certain  portions  of 
the  moon  these  craters 
stand  very  thickly ;  older 
craters  have  been  en- 
croached upon,  or  more 
or  less  completely  obliter- 
ated, by  the  newer,  so  that 
the  whole  surface  is  a 
chaos  of  which  the 
counterpart  is  hardly  to 
be  found  on  the  earth, 
even  in  the  roughest  por- 
tions of  the  Alps.  This 
is  especially  the  case  near 
the  moon's  south  pole.  It 
is  noticeable,  also,  that  as 
on  the  earth  the  youngest 
mountains  are  generally  the  highest,  so  on  the  moon  the  newer 
craters  are  generally  deeper  and  more  precipitous  than  the  older. 

The  height  of  a  lunar  mountain  or  depth  of  a  crater  can  be 
measured  with  considerable  accuracy  by  means  of  its  shadow, 
or,  in  the  case  of  a  mountain,  by  the  measured  distance  between 
its  summit  and  the  terminator  at  the  time  when  the  top  first 
catches  the  light,  looking  like  a  star  quite  detached  from  the 
bright  part  of  the  moon,  as  seen  in  Fig.  73. 


Copernicus. 


Theophilus. 


FIG.  74.  —  Copernicus 


The 

youngest 
craters 
usually  the 


Measure- 
ment of 
elevations 
on  the  moon. 


190 


MANUAL   OF   ASTRONOMY 


Lunar 
craters  are 
probably  of 
volcanic 
origin,  but 
the  explana- 
tion is  not 
free  from 
difficulty. 


No  volcanic 
action  at 
present 
evident  on 
the  moon. 


Rills  and 
clefts. 


Streaks-  or 
rays. 


216.  The  striking  resemblance  of  these  formations  to  terres- 
trial volcanic   structures,  like  those  exemplified  by  Vesuvius 
and  others,  makes  it  natural  to  assume  that  they  had  a  similar 
origin.     This,  however,  is  not  absolutely  certain,  for  there  are 
considerable   difficulties  in  the  way,  especially  in  the  case  of 
what  are  called  the  great   "  Bulwark  Plains."     These  are  so 
extensive  that  a  person  standing  in  the  center  could  not  see 
even  the  summit  of  the  surrounding  ring  at  any  point ;  and  yet 
there  is  no  line  of  discrimination  between  them  and  the  smaller 
craters  —  the  series  is  continuous.     Moreover,  on  the  earth  vol- 
canoes necessarily  require  the  action  of  air  and  water,  which  do 
not  at  present  exist  on  the  moon.     It  is  obvious,  therefore,  that 
if  these  lunar  craters  are  the  result  of  volcanic  eruptions,  they 
must  be,  so  to  speak,  "  fossil "  formations,  for  it  is  quite  certain 
that  there  is  absolutely  no  evidence  of  present  volcanic  activity. 

217.  Other  Lunar  Formations.  —  The  craters  and  mountains 
are  not  the  only  interesting  formations  on  the  moon's  surface. 
There  are  many  deep,  narrow,  crooked  valleys  that  go  by  the 
name  of   "rills,"   some   of  which  may  once  have  been  water- 
courses.    Fig.    74    shows   several   of  them.      Then  there   are 
numerous    straight    "  clefts,"  half  a   mile   or  so  wide  and  of 
unknown  depth,  running  in  some  cases  several  hundred  miles, 
straight  through  mountain  and  valley,  without  any  apparent 
regard  for  the  accidents  of  the  surface :  they  seem  to  be  deep 
cracks  in  the  crust  of  our  satellite.     Most  curious  of  all  are 
the  light-colored  streaks,  or  "  rays,"  which  radiate  from  certain 
of  the  craters,  extending  in  some  cases  a  distance  of  many  hun- 
dred miles.     These  are  usually  from  5  to  10  miles  wide  and 
neither  elevated  nor  depressed  to  any  considerable  extent  with 
reference  to  the  general  surface.      Like  the  clefts,  they  pass 
across   valley  and  mountain,  and  sometimes  through  craters, 
without  any  change  in  width  or  color.     .They  have  been  doubt- 
fully explained  as  a  staining  of  the  surface  by  vapors  ascending 
from  rifts  too  narrow  to  be  visible. 


THE   MOON  191 

The  most  remarkable  of  these  "  ray  systems  "  is  the  one  con- 
nected with  the  great  crater  Tycho,  not  very  far  from  the  moon's  Ray  system 
south  pole,  well  shown  in  the  (nearly)  full-moon  photograph  on  of  Tvcho- 
page  187.     The  rays  are  not  very  conspicuous  until  within  a 
few  days  of  full  moon,  but  at  that  time  they  and  the  crater 
from  which  they  diverge  constitute  by  far  the  most  striking 
feature  of  the  whole  lunar  surface. 

218.  Lunar  Maps. — A  number  of  maps  of  the  moon  have  been  con-  Lunar  maps, 
structed  by  different  observers.  The  most  extensive  is  that  by  Schmidt 
of  Athens,  on  a  scale  7  feet  in  diameter,  published  by  the  Prussian  govern- 
ment in  1878.  Of  the  smaller  maps  available  for  ordinary  lunar  observa- 
tion, perhaps  the  best  is  that  given  in  Webb's  Celestial  Objects  for  Common 
Telescopes.  Two  new  photographic,  large-scale,  lunar  maps  have  lately 
been  published  from  negatives  made  at  the  Lick  and  Paris  observatories. 
Our  maps  of  the  visible  part  of  the  moon  are  on  the  whole  as  complete 
and  accurate  as  our  maps  of  the  earth,  taking  into  account  the  polar 
regions  and  the  interior  of  the  continents  of  Asia  and  Africa. 

219.  Lunar  Nomenclature.  —  The  great  plains  upon  the  moon's  surface   Lunar 
were  called  by  Galileo  "oceans"  or  "seas"  (inaria),  for  he  supposed  that   nomen- 
these  grayish  surfaces,  which  are  visible  to  the  naked  eye  and  conspicuous   clature- 
in  a  small  telescope,  though  not  with  a  large  one,  were  covered  with  water. 

The  ten  mountain  ranges  on  the  moon  are  mostly  named  after  terrestrial 
mountains,  as  Caucasus,  Alps,  Apennines,  though  two  or  three  bear  the 
names  of  astronomers,  like  Leibnitz,  Doerfel,  etc. 

The  conspicuous  craters  bear  the  names  of  eminent  ancient  and  medi- 
eval astronomers  and  philosophers,  as  Plato,  Archimedes,  Tycho,  Coperni- 
cus, Kepler,  and  Gassendi ;  while  hundreds  of  smaller  and  less  conspicuous 
formations  bear  the  names  of  more  modern  astronomers. 

This  system  of  nomenclature  seems  to  have  originated  with  Riccioli, 
who  in  1651  published  a  map  of  the  moon. 

220,  Changes  on  the  Moon.  —  It  is  certain  that  there  are  no  Question  of 
conspicuous   changes  :    there    are    no    such    transformations    as  chan£es  on 

J  '  the  moon's 

would  be  presented  by  the  earth  viewed  telescopically,  —  no  surface, 
clouds,  no  storms,  no  snow  of  winter,  and  no  spread  of  vege-  None  that 

...  ,       are  obvious, 

tation    in   the    spring.      At  the  same   time    it   is    confidently  ^ut  some 
maintained  by  some  observers  that  here  and  there  alterations  probable. 


192 


MANUAL   OF   ASTRONOMY 


do  take  place  in  the  details  of  the  lunar  surface,  while  others 
as  stoutly  dispute  it. 

The  difficulty  in  settling  the  question  arises  from  the  great 
changes  in  the  appearance  of  a  lunar  object  under  varying  illu- 
mination. To  insure  certainty  in  such  delicate  observations, 


FIG.  75.  — Map  of  the  Moon 
Reduced  from  Neison 


Difficulty  of  comparisons  must  be  made  between  the  appearance  of  the  object 
the  problem.   -n  question,  as  seen  at  precisely  the  same  phase  of  the  moon, 
with  telescopes  (and  eyes  too)  of  equal  power,  and  under  sub- 
stantially the  same  conditions  in   other  respects,  such  as  the 
height  of  the  moon  above  the  horizon  and  the  Clearness  and 


THE  MOON  193 

steadiness  of  the  air.  It  is,  of  course,  very  difficult  to  secure  such 
identity  of  conditions.  (For  an  account  of  certain  supposed 
changes,  see  Webb's  Celestial  Objects  for  Common  Telescopes.} 

221,   Fig.  75  is  reduced  from  a  skeleton  map  of  the  moon  by  skeleton 
Neison  and,  though  not  large  enough  to  exhibit  much  detail,  maP°ftlie 
will  enable  a  student  with  a  small  telescope  to  identify  the 
principal  objects  by  the  help  of  the  key. 

KEY  TO   THE   PRINCIPAL  OBJECTS   INDICATED   IN  FIG.  75 

A.  Mare  Humorum.  K.  Mare  Nubium. 

B.  Mare  Nectaris.  L.  Mare  Frigoris. 

C.  Oceanus  Procellarum.  T.  Leibnitz  Mountains. 

D.  Mare  Fecunditatis.  U.  Doerfel  Mountains. 

E.  Mare  Tranquilitatis.  V.  Rook  Mountains. 

F.  Mare  Crisium.  W.  D'Alembert  Mountains, 

G.  Mare  Serenitatis.  X.  Apennines. 
H.  Mare  Imbrium.  Y.  Caucasus. 

7.  Sinus  Iridum.  Z. 


1.  Clavius.                         14.  Alphonsus.  27.  Eratosthenes. 

2.  Schiller.                         15.  Theophilus.  28.  Proclus. 

3.  Maginus.                       16.  Ptolemy.  28'.  Pliny. 

4.  Schickard.                     17.  Langrenus.  29.  Aristarchus. 

5.  Tycho.                           18.  Hipparchus.  30.  Herodotus. 

6.  Walther.                        19.  Grimaldi.  31.  Archimedes. 

7.  Purbach.                      20.  Flamsteed.  32.  Cleomedes. 

8.  Petavius.                      21.  Messier.  33.  Aristillus. 

9.  "  The  Railway."          22.  Maskelyne.  34.  Eudoxus. 

10.  Arzachel.                      23.  Triesnecker.  35.  Plato. 

11.  Gassendi.                      24.  Kepler.  36.  Aristotle. 

12.  Catherina.                     25.  Copernicus.  37.  Endymion. 

13.  Cyrillus.  26.  Stadius. 

222.   Lunar  Photography.  —  It  is  probable  that  the  question  Lunar  pho- 
of  changes  upon  the  moon's  surface  will  in  the  end  be  authori- 

tatively  decided  by  means  of  photography.  The  earliest  success 

in  lunar  photography  was  that  of  Bond  of  Cambridge,  U.S.,  in 


194 


MANUAL   OF   ASTRONOMY 


Originated 
in  this 
country. 


Latest 
successes. 


1850,  using  the  old  daguerreotype  process.  This  was  followed 
by  the  work  of  De  la  Rue  in  England,  and  by  Dr.  Henry  Draper 
and  Mr.  Lewis  M.  Rutherfurd  in  this  country.  Until  very 
recently  Mr.  Rutherfurd's  pictures  have  remained  absolutely 
unrivaled  ;  but  since  1890  there  has  been  a  great  advance.  At 
various  places,  especially  at  Cambridge  and  at  the  Lick  and 
Yerkes  observatories  in  this  country,  and  at  Paris,  most  admi- 
rable photographs  have  been  made,  which  bear  enlargement  well 
and  show  almost  as  much  detail  as  can  be  seen  with  the  telescope, 
—  not  quite,  however. 

The  half-tone  engraving  of  the  entire  moon  on  page  187  is  slightly 
enlarged  from  a  photograph  made  by  Professor  Hale  at  his  Kenwood 
Observatory  (Chicago)  in  1892  with  a  13^-inch  photographic  object-glass. 
The  other  covers  a  small  portion  of  the  moon's  surface  on  a  much  larger 
scale,  including  the  great  crater  Theophilus  with  its  neighbors  Cyrillus 
and  Catherina.  It  is  enlarged  from  a  magnificent  photograph  made  in 
1900  by  Ritchey  of  the  Yerkes  Observatory  with  the  non-photographic 
object-glass  of  the  great  40-inch  telescope,  a  yellowish  color  screen  being 
used  in  front  of  the  sensitive  plate  to  cut  off  the  red,  violet,  and  ultra-violet 
rays,  according  to  the  method  introduced  by  Professor  Hale.  The  original 
negative  is  certainly  not  surpassed  by  any  thus  far  obtained  with  photo- 
graphic lenses  or  reflectors. 


CHAPTER   VIII 
THE  SUN 

Its  Distance,  Dimensions,  Mass,  and  Density — Its  Rotation  and  Equatorial  Accel- 
eration —  Methods  of  studying  its  Surface  —  The  Photosphere  —  Sun-Spots  — 
Their  Nature,  Dimensions,  Development,  and  Motions  —  Their  Distribution  and 
Periodicity  —  Sun-Spot  Theories 

THE  sun  is  the  nearest  of  the  stars,  —  a  hot  self-luminous 
globe,  enormous  as  compared  with  the  earth  and  moon,  though 
probably  only  of  medium  size  compared  with  other  stars ;  but  to 
the  earth  and  the  other  planets  which  circle  around  it  it  is  the 
most  magnificent  and  important  of  all  the  heavenly  bodies.     Its  The  sun's 
attraction  controls  their  motions,  and  its  rays  supply  the  energy  8UPremacy- 
which  maintains  every  form  of  activity  upon  their  surfaces. 

223.   The  Distance  of  the  Sun  ;  the  Astronomical  Unit.  —  The 
problem  of  finding  accurately  the  sun's  distance  is  one  of  the 
most  important  and  difficult  presented  by  astronomy,  —  impor-  importance 
tant  because  this  distance,  i.e.,  the  radius  of  the  earth's  orbit,  is  and  dlffi" 

culty  of 

the  fundamental  Astronomical  Unit  to  which  all  measurements  determining 
of  celestial  distance  are  referred ;  difficult  because  the  measure-  the  distance 
ments  which  determine  it  are  so  delicate  that  any  minute  error  tne  fun(ja- 
of  observation  is  enormously  magnified  in  the  result.  mental 

Without  a  knowledge  of  the  sun's  distance  we  cannot  form  j^j^^~ 
any  idea  of  its  real  dimensions,  mass,  and  density,  and  the 
tremendous  scale  of  solar  phenomena. 

We  have  already  given  one  method  for  finding  this  distance, 
depending  upon  the  experimental  determination  of  the  velocity  Already 
of  light,  combined  with  the  observed  constant  of  aberration,  and  determined 
we  postpone  until  later  the  consideration  of  the  methods  by  tion  of  light, 
which  we  measure  the  sun's  parallax  (Sec.  79)  and  so  determine 

196 


196 


MANUAL   OF   ASTRONOMY 


his  distance  in  terms  of  the  radius  of  the  earth.     From  the 
combination  of  all  the  material  now  available  the  sun's  mean 
its  distance    distance  comes  out  very  closely  92  900000  miles  (149  500000 
mik^000        kilometers),  the  horizontal  parallax  being  8".80  ±  0".02. 

The  distance  is  still  uncertain  by  perhaps  100000  miles,  and 
because  of  the  eccentricity  of  the  earth's  orbit  it  is  variable  to 
the  extent  of  about  3  000000  miles,  being  the  least  on  January  1 
and  greatest  early  in  July. 

The  orbital  velocity  of  the  earth,  found  by  dividing  the  cir- 
cumference of  the  orbit  by  the  number  of  seconds  in  a  year, 
is  18£  miles  a  second,   as   already  determined   by  aberration 
(Sec.  173).     (Compare  this  velocity  with  that  of  a  cannon-shot 
—  seldom  exceeding  2500  feet  per  second.) 

Perhaps  one  of  the  simplest  illustrations  of  the  distance  of  the  sun  is 
that  such  a  shot  would  require  over  six  years  to  reach  the  sun,  traveling 
without  change  of  speed.  A  railroad  train  running  at  60  miles  an  hour, 
without  stop  or  slackening,  would  require  175  years,  and  the  fare  one  way, 
at  two  cents  a  mile,  would  be  $1  860000.  A  bicyclist  traveling  100  miles 
a  day  would  be  nearly  2550  years  in  making  the  journey,  and  if  he  had 
started  from  the  sun  in  the  year  A.D.  1,  he  would  by  this  time  have  covered 
only  about  three  quarters  of  the  distance.  Light  makes  the  journey  in 
499  seconds. 

224.  Dimensions  of  the  Sun.  —  The  sun's  mean  apparent 
diameter  is  32'  4"  ±  2".  Since  at  the  distance  of  the  sun  one 
second  equals  450.36  miles  (92  900000  +  206264.8),  its  real 
diameter  is  866500  miles,  or  109£  times  that  of  the  earth.  It 
is  quite  possible  that  this  diameter  is  variable  to  the  extent 
of  a  few  hundred  miles,  since  the  sun  is  not  solid. 

If  we  suppose  the  sun  to  be  hollowed  out,  and  the  earth 
placed  at  the  center,  the  sun's  surface  would  be  433000  miles 
away.  Now,  since  the  distance  of  the  moon  from  the  earth  is 
about  239000  miles,  she  would  be  only  a  little  more  than  half- 
way out  from  the  earth  to  the  inner  surface  of  the  hollow  globe, 
which  would  thus  form  a  very  good  sky  background  for  the 


THE   SUN 


197 


study  of  the  lunar  motions.  Fig.  76  illustrates  the  size  of  the 
sun,  and  of  such  objects  upon  it  as  the  sun-spots  and  "promi- 
nences," compared  with  the  size  of  the  earth  and  the  moon's 
orbit. 

If  we  represent  the  sun  by  a  globe  2  feet  in  diameter,  the  earth  on 
the  same  scale  would  be  0.22  of  an  inch  in  diameter,  the  size  of  a  very 
small  pea,  at  a  distance  from  the  sun  of  just  about  220  feet ;  and  the 
nearest  star,  still  on  the  same  scale,  would  be  8000  miles  away  at  the  antipodes. 


FIG.  70.  —  Dimensions  of  the  Sun  compared  with  the  Moon's  Orbit 

Since  the  surfaces  of  globes  are  proportional  to  the  squares 
of  their  radii,  the  surface  of  the  sun  exceeds  that  of  the  earth 
in  the  ratio  of  109.52  : 1 ;  i.e.,  the  area  of  its  surface  is  about 
12000  times  the  surface  of  the  earth. 

The  volumes  of  spheres  are  proportional  to  the  cubes  of  their 
radii.  Hence,  the  sun's  volume  (or  bulk)  is  109.53,  or  1  300000, 
times  that  of  the  earth. 

225,  The  Sun's  Mass.  —  This  is  about  333000  times  that  of 
the  earth.  For  our  purpose  the  most  convenient  way  of  reaching 


Surface  area 
of  the  sun 
12000  times 
as  great  as 
that  of  the 
earth.    Bulk 
1300000 
times  as 
great  as  that 
of  the  earth. 


198 


MANUAL   OF   ASTRONOMY 


Mass  of  the    this  result  (for  another  method,  see  Sec.  380)  is  by  comparing 
sun  333000       i  ^  ear^n's  attraction  for  bodies  at  her  surface,  with  the  sun's 

times  that 

of  the  earth,  attraction  for  the  earth  as  measured  by  our  orbital  motion. 
Call  this  attraction  f\  and  let  R  be  the  radius  of  the  earth's 
orbit,  r  the  radius  of  the  earth,  S  the  mass  of  the  sun,  and  E 
that  of  the  earth.  Then,  from  the  law  of  gravitation  (Sec.  146), 


we  have l 


How  deter- 
mined. 


or 


central  force,  /= — , 
R 


in  which  V  is 


But,    from   the   law  of 

18J  miles  a  second  and  R  92  900000  miles.     Reducing  R  and  V 

to  inches,  and  making  the  computation,  we  find/=  0.2332  inches, 

f 
and  since  g  (corrected  for  centrifugal  force)  is  386.8  inches,  -  = 

92  900000 


Earth's 
orbit  departs 
from  a 
straight  line 
only  a  little 
more  than 
one  ninth  of 
an  inch  in 
18.5  miles. 


3958 

is    550  686000.      Finally,    therefore,    S=Ex  Q         = 

Ibo8.7 

332400  E.     But  the  last  three  figures  are  uncertain. 

226.  The  Curvature  of  the  Earth's  Orbit  and  Total  Force  of 
Sun's  Attraction.  --  The  distance  which  the  earth  would  fall 
towards  the  sun  in  a  second  if  its  orbital  motion  were  arrested 
is  J-  /,  or  0.116  inches,  just  as  J-  g,  16^-  feet,  is  the  distance 
a  body  falls  towards  the  earth  in  the  first  second;  and  this 
0.116  inches  is  the  amount  by  which  the  earth  deviates  from  a 
tangent  to  its  orbit  in  a  second.  In  other  words,  the  earth  in 
traveling  18.5  miles  is  deflected  towards  the  sun  but  a  little 
more  than  one  ninth  of  an  inch. 

1  Since  the  attractions  of  the  sun  and  earth  are  here  measured  by  the  acceler- 


ations f  and  g,  the  proportion  would  strictly  be  / :  g  = 


S  +  E   E  +  m 

72~ 


,  where 


m  is  the  small  body  by  the  fall  of  which  g  is  determined.  But  E  and  m  are  so 
small  as  compared  with  S  and  E,  respectively,  that  they  may  be  omitted  without 
sensible  error,  as  in  the  proportion  given.. 


THE   SUN  199 

It  would  seem  that  a  feeble  force  only  would  be  needed  to 
produce  so  slight  a  deviation  from  a  straight  line.  But  since 
the  sun's  attraction  is  I-^Q  g,  a  mass  of  1659  pounds  on  the 
earth  is  attracted  towards  the  sun  with  a  force  of  about  one 
pound.1 

It  follows,  therefore,  that  the  total  attraction  between  the  Total  attrac. 
earth  and  sun  amounts  to  the  amazing  pull  of  3  600000  millions  tion  between 


of  millions  of  tons  (i^g-g-  of  the  earth's  mass,  which  is  6  x  1021  earth  equal 
tons).     This  would  be  the  breaking  strain  of  a  steel  rod  more  to  the 
than  3000  miles   in  diameter,  —  a  force   inexplicably  exerted  strain  of  a 
through,  or  transmitted  by,  apparently  empty  space,  in  which  steel  rod 

,1          n  .,,  .,,  .    ,  3000  miles  in 

the  planets  move  without  sensible  resistance.  diameter 

227,  Superficial  Gravity,  or  Gravity  at  the  Surface  of  the 
Sun.  —  This  is  found  by  dividing  the  sun's  mass  by  the  square 

of  its  radius  (both  compared  with  the  earth),  i.e.,  ^noTo"  2'  wn^cn  Gravity  on 

(109.52)  sun's  sur- 

gives  27.6.     A  mass  of  ten  pounds  would  weigh  276  pounds  face  nearly 
011  the  sun,  and  a  person  who  weighs  150  pounds  here  would  ^e^tason 
weigh  over  two  tons  there.     Locomotion  would  be  impossible,  the  earth. 
A  body  would  fall  444  feet  in  the  first  second,  and  a  pendu- 
lum which  here  vibrates  in  a  second  would  vibrate  in  less  than 
one  fifth  of  a  second  there.     But  (putting  temperature  out  of 
consideration)  a  watch  would  go  no  faster  there  than  here,  since 
neither  the  inertia  of  the  balance-wheel  nor  the  elasticity  of 
the  spring  would  be  affected  by  the  increased  gravity. 

228.  The   Sun's   Density.  —  Its    mean  density  as    compared  Mean 

with  that  of  the  earth  mav  be  found  by  simply  dividing  its  mass  densitv  of 

J  J        f  j  the  sun  only 

by  its  volume  (both  as  compared  with  the  earth)  ;  i.e.,  the  sun  s  about  one 
density   equals    332000  -*-  1  300000  =  0.255,  —  a   little    more  fourth  of 

,1  P    ,1  ,1  •>       i  tne  earth's 

than  one  quarter  of  the  earth  s  density.  density,  or 

1.4  times 

1  This  does  not  imply,  and  it  is  not  true,  that  when  the  sun  is  overhead  a  166-   that  of 
pound  man  weighs  one  tenth  of  a  pound  less  (by  a  spring-balance)  than  when   water. 
the  sun  is  rising.     (Why  not  ?)     The  difference  is  really  only  about  20  Oooooo 
of  his  weight  (Sec. 


200 


MANUAL   OF   ASTRONOMY 


To  get  its  specific  gravity  —  its  density  compared  with  water  — 
we  must  multiply  this  by  the  earth's  mean  specific  gravity, 
5.53,  which  gives  1.41.  That  is,  the  sun's  mean  density  is  less 
than  one  and  one-half  times  that  of  water. 

This  is  a  most  remarkable  and  significant  fact,  considering  the 
sun's  tremendous  force  of  gravity  and  that  a  considerable  portion 
of  its  mass  is  composed  of  metals,  as  proved  by  the  spectroscope. 
The  obvious,  and  only  possible,  explanation  is  that  the  tempera- 
ture of  the  sun  is  such  that  its  materials  are  almost  wholly  in 

the  condition  of  vapor,  —  not 
solid  or  even  liquid. 

229.  The  Sun's  Rotation.  — 
This  is  made  evident  by  the 
behavior  of  the  dark  sun-spots 
which  cross  the  sun's  disk  from 
east  to  west.  The  times  in 
which  they  make  their  circuits 
differ  slightly,  but  the  aver- 
age, as  seen  from  the  earth, 
is  27.25  days.  This,  however, 
is  not  the  true  or  sidereal  time 
of  the  sun's  rotation,  but  the 


Equation  for 
determining 
the  sidereal 
period  from 
the  synodic. 


FIG.  77. —  Synodic  and  Sidereal  Revolu- 
tion of  the  Sun 


synodic,  as  is  evident  from 
Fig.  77.  Suppose  that  an  observer  on  the  earth  at  E  sees  a  spot 
on  the  center  of  the  sun's  disk  at  S\  while  the  sun  rotates  the 
earth  will  also  move  forward  in  its  orbit,  and  when  he  next  sees 
the  spot  on  the  center  of  the  disk  he  will  be  at  E',  the  spot 
having  gone  around  the  whole  circumference  plus  the  arc  SS'. 
The  equation  by  which  the  true  period  is  deduced  from  the 
synodic  is  the  same  as  in  the  case  of  the  moon,  viz., 

11-1 

T      E~  S* 

T  being  the  true  sidereal  period  of  the  sun's  rotation,  E  the 
length  of  the  year,  and  S  the  observed  synodic  rotation.     This 


THE   SUN  201 

gives  T  =  25.35  days.    In  a  year  the  number  of  sidereal  revolu-  Sidereal 
tions  exceeds  that  of  the  synodic  by  exactly  one.  period  about 

Different  observers,  however,  get  slightly  different  results, 
because  the  spots  are  not  fixed  in  their  positions  on  the  sun's 
surface.  Carrington  finds  25.38  days  and  Spoerer  25.23  days. 

The  paths  of  the   spots   across  the  sun's   disk  are  usually 
more  or  less  oval,  showing  that  the  sun's  axis  is  not  perpen-  inclination 
dicular  to  the  ecliptic,  but  so  inclined  that  the  north  pole  is  ofsun's 
tipped  a  little  more   than  7°  towards  the  position  which  the  the  ecliptic 
earth  occupies  on  September  7.     The  inclination  of  the  sun's  ab<>ut70. 
equator  to  the  plane  of  the  terrestrial  equator  is  about  26°  15'; 
but  different  investigators  get  slightly  different  values. 

The  position  of  the  point  in  the  sky  towards  which  the  sun's  Position  of 
axis  is  directed  is  the  8un's 

.    .  .  J — .  ^ — _ /  _i  pole  in  the 

in  right  ascension    /*  ^        /^_^,       ^    X         /^\    heavens. 

19h,     declination 

+   63°   45f,  very 

nearly   half-way        DEC.  MARCH  JUNE  SEPT< 

Ti  &  i"  \v  f*  f*  TI       i"  n  P 

FIG.  78.  — Path  of  Sun-Spots  across  the  Sun's  Disk 
bright  star  a  Lyrs6 

and  the  pole-star.  Twice  a  year,  when  the  earth  is  in  the  plane  Dates  when 
of  the  sun's  equator,  the  sun-spot  paths  become  straight,  —  on  earthPasses 
June  3  and  December  5.  (See  Fig.  78.)  the  sun's 

230.  The  Equatorial  Acceleration.  —  It  was  noticed  quite  early  e(iuator- 
that  different  spots  give  different  results  for  the  period  of  rota- 
tion, but  the  researches  of  Carrington  about  1860  first  brought 
out  the  fact  that  the  differences  are  systematic,  and  that  at  the 
solar  equator  the  time  of  rotation  is  shorter  than  on  either  side  of 
it.  For  spots  near  the  sun's  equator  it  is  about  twenty-five 
days;  in  solar  latitude  30°,  twenty-six  and  one-half  days;  and 
in  solar  latitude  40°,  twenty-seven  days.  In  latitude  45°  it  is  The  sun's 
fully  two  days  longer  than  at  the  equator ;  but  we  are  unable 
to  carry  the  observations  to  higher  latitudes  because  spots 
almost  never  appear  beyond  the  parallels  of  45°. 


202 


MANUAL   OF   ASTRONOMY 


Formulse  for  Various  formulae  have  been  proposed  to  represent  the  motion  ;  that  of 
sun's  rate  of  Faye,  which  agrees  with  the  observations  as  well  as  any,  is  X  =  862'  — 
rotation  in  186' sin2/,  X  being  the  daily  motion.  Spoerer's  formula,  as  modified  by 
Wolfer,  is  X  =  8°.55  +  5°. 80  cos  I.  This  looks  very  different  from  Faye's, 
but  gives  very  nearly  the  same  results  for  the  regions  in  which  spots  are 
observable.  None  of  the  formulae  proposed  rest  on  any  sound  theoretical 
explanation. 


different 
solar  lati 
tudes. 


Sun's  sur- 
face not 
solid. 


Cause  of 

equatorial 

acceleration 

not  yet 

certainly 

ascertained. 

Probably  a 

survival 

from  past 

conditions. 


Arrange- 
ments for 
study  of 
sun's  sur- 
face. 


Telescope 
and  screen. 


FIG.  79.  —  Telescope  and  Screen 


Clearly  the  sun's  visible  surface  is  not  solid,  but  permits 
motions  and  currents  like  those  of  our  air  and  oceans.  It 
might  be  argued  that  the  spots  misrepresent  the  sun's  real  rota- 
tion, not  being  fixed  upon  its  surface,  floating  like  our  clouds. 
The  faculae,  however,  give  substantially  the  same  result,  and  so 

do  recent  spectroscopic  observa- 
tions of  the  shift  of  lines  in  the 
spectrum  at  the  eastern  and  western 
limbs.  (See  Sec.  254.) 

Possibly  this  equatorial  acceler- 
ation may  be,  in  some  way,  an  effect 
of  the  tremendous  outpour  of  heat 
from  the  solar  surface,  as  Emden 
of  Munich  attempts  to  show  in  a 
paper  just  published.  Other  recent  investigators,  however, 
have  reached  the  conclusion  that  it  cannot  be  explained  by 
causes  now  acting,  but  is  a  lingering  survival  from  the  surfs 
past  history,  and  destined  ultimately  to  disappear. 

231.  Arrangements  for  the  Study  of  the  Sun's  Surface — The 
heat  and  light  of  the  sun  are  so  intense  that  we  cannot  look 
directly  at  it  with  a  telescope.  A  very  convenient  method  of 
exhibiting  the  sun  to  a  number  of  persons  at  once  is  simply  to 
attach  to  a  telescope  a  small  frame  carrying  a  screen  of  white 
paper  at  a  distance  of  a  foot  or  more  from  the  eyepiece,  as 
shown  in  Fig.  79.  A  screen  should  also  be  used  at  the  object 
end,  as  shown  in  the  figure,  in  order  to  shade  the  paper  upon 
which  the  image  is  formed.  When  the  focus  is  properly 


THE   SUN 


203 


a 


adjusted  a  distinct  image  appears,  which  shows  the  sun's  princi- 
pal features  very  fairly  ;  indeed,  with  proper  precautions,  almost 
as  well  as  the  most  elaborate  apparatus.  Still,  it  is  generally 
more  satisfactory  to  look  at  the  sun  directly  with  a  suitable 
eyepiece. 

With  a  small  telescope,  not  more  than  2-J-  or  3  inches  in  Solar  eye- 
diameter,  a  simple  shade  glass  is  often  used  between  the  eye- 
piece  and  the  eye;  but  the  dark  glass  soon  becomes  very  hot  scopes. 
and  is  apt  to  crack.     With  larger  instruments  it  is  necessary 
to  use  eyepieces  specially  designed  for  the  purpose,  and  known 
as  solar  eyepieces,  or  helioscopes,  which  reject  most  of  the  light 
coming   from   the    object-glass    and 
permit  only  a  small  fraction  of  it  to 
enter  the  eye. 

The  simplest  of  them,  and  a  very  good 
one,  is  known  as  HerschePs,  in  which  the 
sun's  rays  are  reflected  at  right  angles  by 
a  plane  of  unsilvered  glass.  The  reflector 
is  made  wedge-shaped,  as  shown  in  Fig.  80, 
in  order  that  the  reflection  from  the  back 
surface  may  not  interfere  with  the  image. 
Most  of  the  light  passes  through  the  glass 
and  out  through  the  open  end  of  the  eye- 
piece, but  the  reflected  light  is  still  too 
intense  for  the  unprotected  eye.  Only  a  thin  shade  glass  is  required,  how- 
ever, which  does  not  become  very  much  heated.  A  more  elaborate  polar- 
izing helioscope,  figured  in  the  General  Astronomy,  is  still  better. 

It  is  not  a  good  plan  to  cap  the  object-glass  in  order  to  reduce 
the  light.  To  cut  down  the  aperture  is  to  sacrifice  the  defini- 
tion of  delicate  details  (Sec.  46). 

232.   The  Heliograph.  —  In  the   study  of  the  sun's  surface, 
photography  is  for  some  purposes  very  advantageous  and  much  Solar  pho- 
used.     The  instrument  (called  a  heliograph)  must,  however,  have  tosraPhy  >' 

tJlG  D.6ilO~ 

lenses  specially  constructed  for  photography,   since  a  visual  graph. 
object-glass  would  be  nearly  worthless  for  the  purpose  unless 


FIG.  8(jk  —  Herschel  Eyepiece 


204  MANUAL   OF   ASTRONOMY 

possibly  the  use  of  a  color  screen  might  make  it  available 
(Sec.  222).  Arrangements  must  be  made  also  to  secure  an 
extremely  rapid  exposure,  and  it  is  best  to  use  special  slow 
plates.  The  disk  of  the  sun  on  the  negatives  is  usually  from 
2  to  10  inches  in  diameter,  but  photographs  of  small  portions 
of  the  solar  surface  are  often  made  on  a  very  much  larger  scale. 


FIG.  81.  —  Greenwich  Photograph  of  Sun-Spot,  Sept.  10,  1898 

Fig.  81  is  reduced  from  a  9-inch  photograph  made  with  one  of 
the  heliographs  at  Greenwich,  on  Sept.  10,  1898. 

Advantages  Photographs  have  the  great  advantage  of  freedom  from  pre- 
auddisad-  possession  on  the  part  of  the  observer,  and  in  an  instant  of 
of^hotog-  time  secure  a  picture  of  the  whole  surface  of  the  sun  such  as 
raphy.  would  require  hours  of  labor  for  a  skilful  draftsman.  On  the 


THE  SUN  205 

other  hand,  they  take  no  advantage  of  the  instants  of  fine  seeing, 
but  offer  merely,  as  some  one  puts  it,  "a  brutal  copy  "  of  what- 
ever happened  to  appear  when  the  plate  was  exposed,  affected  by 
all  the  momentary  distortions  due  to  atmospheric  disturbance. 

233.  The  Photosphere.  —  The  sun's  visible  surface  is  called  The  photo- 
the  Photosphere,  i.e.,  the  "light  sphere."     When  studied  with  sPhere:  5ts 

T  appearance 


FIG.  82.  —  Nodules  and  Granules  on  the  Sun's  Surface 
After  Langley 

a  telescope  under  favorable  conditions,  and  a  rather  low  power, 
it  appears  not  smoothly  bright,  but  mottled,  looking  much  like 
rough  drawing-paper.  It  is  considerably  darker  at  the  edge  than 
in  the  center,  the  difference  between  the  center  and  limb  being 
especially  conspicuous  in  photographs,  as  in  Fig.  81.  With  a 
high  power  and  the  best  atmospheric  conditions,  the  surface  is 


206 


MANUAL   OF   ASTRONOMY 


The  photo- 
sphere prob- 
ably a  stratum 
of  incandes- 
cent clouds, 
acting  like 
a  Welsbach 
mantle. 


shown  to  be  made  up,  as  seen  in  Fig.  82,  of  a  comparatively 
darkish  background  sprinkled  over  with  grains,  or  "  nodules," 
as  Herschel  calls  them,  of  something  much  more  brilliant,  — 
"  like  snowflakes  on  gray  cloth,"  according  to  Langley.  These 
nodules,  or  "rice  grains,"  are  from  400  to  600  miles  across, 
and  when  the  seeing  is  best  they  themselves  break  up  into 
"  granules "  still  more  minute.  Generally  the  nodules  are 
about  as  broad  as  they  are  long,  though  irregular,  but  here 
and  there,  especially  in  the  neighborhood  of  the  spots,  they  are 
drawn  out  into  long  streaks,  and  then  are  called  "filaments," 

"willow    leaves,"    or 
"thatch  straws." 

Certain  bright 
streaks  and  patches 
called  Faculce  are  also 
usually  visible  here 
and  there  upon  the 
sun's  surface,  and 
though  not  very  ob- 
vious near  the  center 
of  the  disk,  they  be- 
come conspicuous 
near  the  limb,  espe- 
cially in  the  neighborhood  of  spots,  as  shown  in  Fig.  83.  Prob- 
ably they  are  of  the  same  nature  as  the  rest  of  the  photosphere, 
only  elevated  above  the  general  level  and  intensified  in  bright- 
ness because  less  affected  by  the  absorption  of  the  overlying 
gases. 

The  photosphere  is  probably,  according  to  the  view  now 
generally  accepted,  a  sheet  of  clouds  floating  in  a  less  luminous 
atmosphere,  just  as  the  clouds  formed  by  the  condensation  of 
water  vapor  float  in  our  air.  It  is  intensely  brilliant,  for  the 
same  reason  that  the  mantle  of  a  Welsbach  burner  outshines 
the  gas  flame  which  heats  it;  the  radiating  power  of  the  solid 


FIG.  83.  —  Spots  and  Faculae 
After  De  la  Rue 


THE   SUN 


207 


;^:M^  •^' 


and  liquid  particles  which  compose  the  clouds  is  extremely  high 
as  compared  with  that  of  the  gases  in  which  they  float.  (See 
also  Sec.  278.) 

234.  Sun-Spots.  —  Sun-spots,  whenever  visible,  are  the  most 
conspicuous  and  interesting  objects  upon  the  solar  surface. 
The  appearance  of  a  normal  sun-spot  (Fig.  84),  fully  formed 
and  not  yet  beginning  to  break  up,  is  that  of  a  dark  central 
umbra,  with  a  fringing  penumbra  composed  of  converging  fila- 
ments. The  umbra  itself 
is  not  uniformly  dark 
throughout,  but  is  over- 
laid with  filmy  clouds, 
which  usually  require  a 
good  helioscope  to  make 
them  visible,  but  some- 
times, though  rather 
infrequently,  are  c  o  n- 
spicuous,  as  in  the  figure. 
Usually,  also,  within  the 
umbra  there  are  a  num- 
ber of  round  and  very 
black  spots,  sometimes 
called  "  nucleoli,"  but 
often  referred  to  as 
"Dawes'  holes,"  after  the 

name  of  their  first  discoverer.  Even  the  darkest  portions  of  the 
sun-spot,  however,  are  dark  only  by  contrast.  Photometric 
observations  show  that  the  umbra  gives  about  one  per  cent  as 
much  light  as  a  corresponding  area  of  the  photosphere,  so  that 
the  blackest  portion  of  a  sun-spot  is  really  more  brilliant  than  a 
calcium  light  (Sec.  265). 

Very  few  spots  are  strictly  normal.  They  are  often  gathered 
in  groups  within  a  common  penumbra,  which  is  partly  covered 
with  brilliant  "  bridges "  extending  across  from  the  outside 


The  normal 
spot. 


Penumbra, 
umbra, 
nucleoli,  etc 


FIG.  84.  —  Normal  Sun-Spot 
After  Secchi 


Darkest 
part  of  sun- 
spot  as 
bright  as  a 
calcium 
light. 


208 


MANUAL   OF   ASTRONOMY 


Irregulari- 
ties in 
sun-spots. 


Sun-spots 
believed  to 
be  usually 
depressions 
in  the  photo- 
sphere. 


photosphere.  Frequently  the  umbra  is  not  in  the  center  of 
the  penumbra,  or  has  a  penumbra  on  one  side  only;  and  the 
penumbral  filaments,  instead  of  converging  regularly  towards 
the  nucleus,  are  often  distorted  in  every  conceivable  way. 
Fig.  85  is  enlarged  from  a  Greenwich  photograph  of  the 
spot  of  September,  1898. 

235.   Nature  of  Sun-Spots Until  very  recently  sun-spots 

have  been  believed  to  be  cavities  in  the  photosphere  filled  with 
gases  and  vapors,  cooler,  and  therefore  darker,  than  the  sur- 
rounding region.  This  theory  is  founded  on  the  fact  that 


FIG.  85.  —  Group  of  Spots  from  a  Greenwich  Photograph,  Sept.  11,  1898 

many  spots  as  they  cross  the  sun's  disk  behave  as  shown  in 
Fig.  86.  Near  the  limb  they  look  just  as  they  would  if  they 
were  saucer-shaped  hollows,  with  sloping  sides  colored  gray 
and  the  bottom  black. 

This  theory  has,  however,  of  late  been  seriously  called  in 
question ;  many  spots,  possibly  a  majority,  as  shown  by  photo- 
graphs and  drawings,  fail  to  present  the  appearances  described. 
But  the  principal  objection  lies  in  the  behavior  of  spots  in 


THE   SUN  209 

respect  to  their  heat  radiation.     Near  the  center  of  the  disk  Evidence 
the  thermopile  shows  that,  as  they  are  darker,  so  also  they  thatin 
emit  less  heat  than  the  photosphere  around  them ;  but  near  the  they  are 
"  limb  "  (i.e.,  the  edge  of  the  sun's  disk)  the  difference  becomes  elevated 
less  and  in  some   cases  is  even  reversed,  a  fact  most  easily 
explained  by  supposing  the  spot  to  be  high  above  the  photo- 
sphere. 

On  the  whole,  it  now  seems  most  probable  that  different  spots 
lie  at  very  different  levels,  some  low  down,  forming  hollows  in 
the  photosphere,  but  others  at  a  considerable  elevation. 

The  penumbra  is  usually  composed  of  "thatch  straws,"  or  The 
long-drawn-out  filaments  of  photospheric  cloud,  and  these,  as  penumbra. 


FIG.  86.  —  Sun-Spots  as  Cavities 

has  been  said,  converge  in  a  general  way  towards  the  center  of 
the  spot,  though  not  infrequently  more  or  less  spiral  in  their 
course. 

At  its  inner  edge  the  penumbra,  from  the  convergence  of 
these  filaments,  is   usually  brighter  than  at  the  outer.      The  Terminal 
inner   ends   of  the   filaments   are   ordinarily  club-formed;  but  formof 

penumbral 

sometimes  they  are  drawn  out  into  fine  points,  which  seem  to  filaments, 
curve  downward  into  the  umbra,  like  the  rushes  over  a  pool  of 
water.  The  outer  edge  of  the  penumbra  is  usually  pretty 
sharply  bounded,  and  there  the  penumbra  is  darkest.  In 
the  neighborhood  of  the  spot  the  surrounding  photosphere  is 
usually  much  disturbed  and  elevated  into  faculse,  which  ordi- 
narily appear  before  the  spot  is  formed  and  continue  after  it 
disappears. 


210 


MANUAL   OF   ASTRONOMY 


Size  of 
sun-spots. 


Sometimes 
visible  to 
the  naked 
eye. 


Duration  of 
sun-spots 
and  faculae. 


Tendency  of 
sun-spots  to 
recur  at 
points  on 
sun's  surface 
where  spots 
have  dis- 
appeared. 

Initial  stage 
in  life  of  a 
sun-spot. 


Cortie's 
account  of 
the  later 

stages. 


236.  Dimensions  of  Sun-Spots.  —  The  diameter  of  the  umbra 
of  a  sun-spot  varies  all  the  way  from  500  miles,  in  the  case  of 
a  very  small  one,  to  40000  or  50000  miles,  in  the  case  of  the 
largest.     The  penumbra  surrounding  a  group  of  spots  is  some- 
times 150000  miles  across,  though  that  is  exceptional.     Not 
infrequently  sun-spots  are  large    enough  to  be  visible  with  the 
naked  eye  and  can  actually  be  thus  seen  at  sunset  or  through  a 
fog  or  by  the  help  of  a  colored  glass. 

The  Chinese  have  many  records  of  such  objects,  but  their  real 
discovery  dates  from  1610,  as  an  immediate  consequence  of 
Galileo's  invention  of  the  telescope.  Fabricius  and  Scheiner, 
however,  share  the  honor  with  him  as  being  independent 
observers. 

237.  Duration,   Development,  and  Changes  of  Spots.  —  The 
duration   of  sun-spots  is  very  variable ;  but  they  are  always, 
astronomically  speaking,  short-lived  phenomena,  sometimes  last- 
ing for  a  few  days  only,  though  more  usually,  if  of  any  size,  for 
two  or  three  months.     In  a  single  recorded  instance  (1840-41) 
a  spot  persisted  for  eighteen  months. 

The  faculse  in  the  surrounding  region  generally  endure  much 
longer  than  the  spots,  and  not  infrequently  a  new  group  of 
spots  breaks  out  in  the  same  region  where  one  has  disappeared 
some  time  before,  —  as  if  the  local  disturbance  which  caused  the 
spots  andfaculce  still  continued  deep  below  the  surface. 

The  development  of  a  spot  or  spot  group  usually  begins, 
according  to  Secchi,  with  the  formation  of  faculse  interspersed 
with  small  dark  points,  or  "  pores."  These  pores  grow  rapidly 
larger,  coalesce,  and  the  neighboring  "  granules  "  of  the  photo- 
sphere are  transformed  into  the  filaments  of  the  penumbra, 
converging  towards  the  umbra.  Ordinarily  this  process  takes 
several  days,  but  sometimes  only  a  few  hours. 

According  to  Cortie,  the  irregular  group  of  scattered  incipient 
spots  soon  passes  into  a  second  stage,  stretching  out  east  and 
west  with  two  predominant  spots,  one  a  leader,  the  other  a 


THE  SUN  211 

rear-guard  of  the  flock.  The  preceding  one  (in  the  direction  of 
the  sun's  rotation)  is  usually  more  compact  and  regular,  though 
the  other  is  sometimes  the  larger.  The  leader  apparently 
pushes  forward  upon  the  photosphere  and  so  increases  the 
length  of  the  train  of  "  spotlets  "  between  the  two  principals. 
Then  a  third  stage  follows,  as  well  shown  in  Fig.  85,  Sec.  234. 
After  a  time  these  small  spots  generally  disappear,  usually 
followed  pretty  soon  by  the  larger  spot  in  the  rear,  leaving  the 
leader  to  settle  down  into  a  well-formed  "normal"  spot,  which 
may  endure  without  much  change  for  weeks  or  months ;  not 
infrequently,  however,  the  leader  disappears  with  the  rest. 
Frequently  a  large  spot  divides  into  several,  separated  by  bril- 
liant bridges,  and  the  "segments"  fly  apart  with  a  speed  of  Segmenta- 
sometimes  a  thousand  miles  an  hour.  An  active  spot  is  an  tlonofsPots 
extremely  interesting  telescopic  object ;  not  infrequently  a 
single  day  works  a  complete  transformation. 

When  a  large  spot  vanishes  it  is  most  usually  by  the  rapid 
encroachment  of  the  surrounding  atmosphere,  which  seems,  as 
Secchi  expresses  it,  to  "  tumble  pell-mell  into  the  cavity,"  if  it 
be  one,  forming  afacula  to  replace  the  spot. 

238.   Proper  Motions  of  the  Spots.  —  Spots  within  15°  of  the 
equator  usually  drift  slightly  towards  it,  while  those  in  higher  Drift  of  sun- 
latitudes  drift  from  it ;  but  the  drift  in  latitude  is  seldom  rapid,  spots  in 

'    latitude. 

and  exceptions  to  the  rule  are  numerous. 

Active  spots  as  a  rule  drift  pretty  steadily  forward  in  the 
direction  of  the  sun's  rotation.     The  quiet  ones  move  slowly,  Eastward 
if  at  all.     Within  and  close  around  the  spot  the  motion  with  drift  of 

active  spots 

reference  to  the  spot  is  usually  inward  and  downward,  so  far  as 

it  can  be  observed.     Occasionally  fragments  of  the  penumbral  Vertical 

filaments  break  off,  move  towards  the  center  of  the  spot,  and  J^^^rd 

disappear  as  if  swallowed  up  by  a  vortex  (but  there  are  other  in  umbra, 

possible  explanations  of  their  vanishing,  such  as  dissolving  into  uP^ard  " 

invisible  vapor).     Sometimes,  but  rarely,  the  downward  motion  outside  the 

in  the  umbra  of  a  spot  is  swift  enough  to  be  detected  by  the  Penuml)ra> 


212 


MANUAL   OF   ASTRONOMY 


displacement  of  lines  in  the  spectrum  (Sec.  254).  On  the  other 
hand,  around  the  outer  edges  of  the  penumbra  there  is  often  a 
vigorous  boiling  up  from  below,  evidenced  by  the  eruption  of 
prominences  (Sec.  260)  and  by  spectroscopic  phenomena  within 
the  spot  itself.  Cyclonic  action  is  often  observed  ;  sometimes 
there  are  two  or  more  "  whirlpools  "  within  the  same  spot,  not 
infrequently  rotating  in  opposite  directions. 

239.  Distribution  of  the  Spots.  —  For  the  most  part  the  spots 
are  confined  to  two  belts  between  5°  and  40°  of  north  and  south 
latitude  (Fig.  87).  A  few  appear  near  the  equator  at  the  time 
of  the  sun-spot  maximum,  and  practically  none  beyond  the 
forty-fifth  degree,  though  in  somewhat  higher  latitudes  what 


December  6th 


March 


September  5th 


FIG.  87.  —  Spot  Belts  and  Paths 


Trouvelot  calls  "  veiled  spots  "  sometimes  appear,  looking  like 
dark  masses  floating  a  little  below  the  surface  of  the  photo- 
sphere and  only  dimly  seen  through  the  overlying  cloud. 

Generally  the  numbers  are  about  equal  in  the  two  hemispheres,  but 
sometimes  there  is  a  marked  difference  for  years.  From  1672  to  1704 
not  a  single  spot  was  observed  on  the  northern  hemisphere,  and  the  break- 
ing out  of  a  few  in  1705  occasioned  great  surprise  and  was  reported  to 
the  French  Academy  as  an  anomaly.  No  reason  for  such  a  one-sided 
inactivity  has  thus  far  been  discovered. 

Periodicity  240.   Sun-Spot  Periodicity.  —  The    number    of    spots    varies 

of  sun-  greatly  in  different  years  and  shows  an  approximately  regular 

eleven-year  periodicity  of  about  eleven  years.     The  fact  was  first  discov- 

cycie.  ere(j  b     Schwabe  of   Dessau,  in  1843,   as  the   result  of   his 


THE   SUN 


213 


systematic  watching  of  sun-spots  for  nearly  twenty  years,  and 
has  since  been  abundantly  confirmed. 

Wolf  of  Zurich,  who  died  in  1893,  has  collected  all  the  obser- 
vations available  and  summarized  them  in  the  diagram  of  which 
Fig.  88  is  the  reproduction.  Fig.  89  continues  it  to  1905.  The 


ISO 


1UO 


ioob 


Got* 


8  a 


FIG.  88.  —  Wolf's  Sun-Spot  Numbers 

last  maximum  occurred  in  1905 ; 
the  last  minimum  near  the  begin- 
ning of  1901. 

During  the  maximum,  the  sur- 
face of  the  sun  is  never  free 
from  spots ;  sometimes  a  hundred 
are  visible  at  once.  During  the 
minimum,  weeks,  and  months 

even,  pass  without  a  single  one.  The  rise  from  minimum  to 
maximum  is  much  more  rapid  than  the  fall  that  follows,  and 
evidently  from  the  diagram  the  maxima  are  not  of  equal  inten- 
sity, nor  are  their  intervals  equal.  Dr.  J.  S.  Lockyer  (son  of 
Sir  Norman),  from  a  recent  investigation  of  all  data  (including 


100-  - 

i  * 
j, 

S 

I 

j 

\ 
J 

\ 

-4- 

»:*:: 

\ 

_  ^ 

^ 

^ 

—  • 

"^ 

^ 

1880 

1890                         19 

00 

214 


MANUAL   OF   ASTRONOMY 


magnetic  as  well  as  strictly  solar)  between  1833  and  1901,  finds 
that  this  variation  appears  to  be  itself  periodical,  with  a  period 
of  about  thirty-five  years.  But  the  time  covered  by  the  material 
is  hardly  sufficient  to  warrant  a  sure  conclusion. 

Many  attempts  have  been  made  to  connect  these  phenomena 
in  some  way  with  planetary  action,  but  so  far  without  success, 
and  the  general  impression  has  lately  been  that  it  is  probably 
due  to  causes  within  the  sun  itself  or  its  atmosphere  —  a  sort  of 
geyser-like  action  —  rather  than  to  anything  external. 

But  a  recent  thorough  investigation  by  Professor  Newcomb 
puts  rather  a  different  phase  upon  the  matter.  He  finds  a 
regular  period  of  11.13  years  (4.62  +  6.51)  as  a  uniform  cycle 
underlying  the  periodic  variations  of  sun-spot  activity ;  just  as 
the  regular  period  of  36  5  J  days  underlies  the  more  or  less  vari- 
able seasons.  He  adds,  "  Whether  the  cause  of  this  cycle  is 
to  be  sought  in  something  external  to  the  sun,  or  within  it,  ... 
we  have  at  present  no  way  of  deciding." 

241.  Spoerer's  Law  of  Sun-Spot  Latitudes. — Speaking  broadly, 
the  disturbance  which  produces  the  spots  of  a  given  period  first 
appears  in  two  belts,  about  30°  north  and  south  of  the  sun's 
equator.      These    seats    of   disturbance    then    move   gradually 
towards  the  equator,  and  the  spot  maximum  occurs  when  their 
latitude  is  about  16°,  while  the  disturbance  dies  out  at  a  lati- 
tude of  from  5°  to  10°,  about  thirteen  or  fourteen  years  after 
its  first  outbreak.     Two  or  three  years  before  this  disappear- 
ance, however,  two  new  zones  of  disturbance  show  themselves 
in  latitude  30°  to   35°.      Thus,   at  the  spot  minimum  there 
are  usually  four  well-marked  spot  belts,  one  on  each  side  of 
the  equator,  due  to  the  expiring  disturbance,  and  two  in  high 
latitudes,  due  to  the  one  just  beginning. 

242.  Cause  of  Sun-Spots.  —  Absolute  knowledge  is  wanting 
here.     Numerous  theories  have  been  proposed ;  many  of  them 
are  now  refuted,  and  of  those  that  remain  no  one  can  be  said 
to  be  fully  established.     On  the  whole,  perhaps,  at  present  the 


THE   SUN  215 

most  probable  view  is  that  they  are  the  result  of  eruptions,  — 

not,  however,  that  they  are  craters  through  which  the  eruptions 

break  out,  as  was  at  one  time  thought.     It  is  more  likely  that 

when  an  eruption  takes  place  a  hollow  or  "  sink  "  results  in  the  The  theory 

neighboring  surface  of  the  photosphere,  in  which  hollow  the  oferuPtlons 

cooler  gases  and  vapors  collect. 

Another  theory,  first  proposed  by  Sir  John  Herschel  and  now 
favored  by  Lockyer  and  others,  is  that  the  spots  are  formed, 
not  by  any  action  from  within,  but  by  cool  matter  descending  Theory  that 
from   above,   and  probably  of  meteoric  origin;  but  it  is  not  tneyaredue 

.,         ,  .  •  1        i  T          ?  /.  to  meteors. 

easy  to  reconcile  this  with  the  peculiar  distribution  of  the 
spots  upon  the  sun's  surface,  though  it  falls  in  well  with  their 
periodicity. 

Faye  considered  them  to  be  cyclones  1  in  the  solar  atmosphere 
somewhat  analogous  to  terrestrial  storms. 

In  1894   E.   Oppolzer  of  Vienna  proposed  the  newest  theory,  which   Meteoro- 
attributes  them  to  bodies  of  gas  and  vapor  which,  ascending  from  the 


polar  regions,  drift  towards  the  equator  and  descend  in  the  spot  zones,  *  e01  ies* 
becoming  warmed  and  dried  by  the  descent,  —  just  as  is  the  case  with 
descending  currents  in  the  earth's  atmosphere.  If  he  is  right,  the  spots 
are  actually  hotter  than  the  underlying  photosphere,  but  less  luminous 
because,  being  purely  gaseous,  they  radiate  less  powerfully. 

243,   Terrestrial    Influence   of    Sun-Spots.  —  One    correlation  The  terres- 
between  sun-spots  and  the  earth  is  perfectly  proved.     When  the  trial  influ" 

J  *  enceof 

spots  are  numerous  magnetic  disturbances  ("magnetic  storms'')  sun-spots. 
are  most  numerous  and  intense,  and,  as  Ellis  has  also  showed, 
the  regular  daily  variations  of   terrestrial  magnetism  are  also 
greatest  ;   in   many  instances   also  (but  by  no  means  always) 
notable  disturbances  upon  the  sun  have  been  accompanied  by 
violent  magnetic  storms  and  electric  earth-currents,  with  brilliant  Correlation 
exhibitions  of  the  aurora  borealis,  as  in  1859  and  1883.     The  ofterrestrial 

magnetic 

fact  of  the  connection  between  terrestrial  magnetism  and  solar  disturbances 
disturbances  is  beyond  doubt,  though  the  nature  and  mechanism  with  sun~ 
of  this  connection  is  as  yet  unknown,  —  we  do  not  know  whether 

i  See  note  on  page  260. 


216 


MANUAL   OF   ASTRONOMY 


the  solar  disturbance  causes  the  terrestrial,  or  whether  both  dis- 
turbances are  due  to  some  external  influence. 

The  dotted  lines  in  Figs.  88  and  89  represent  the  magnetic 
"  storminess "  at  the  indicated  dates,  and  its  correspondence 
with  the  sun-spot  curve  makes  it  impossible  to  doubt  their 
connection. 

It  has  also  been  attempted  to  show  that  solar  disturbances 

are  accompanied  by  effects  upon  the  earth's  meteorology, — upon 

Question  of    its  temperature,  barometric  pressure,  storminess,  and  amount  of 

effect  upon     rainfall>     jt   can  only  be  said  tnat  tne   matter  is  still  under 

the  meteor- 
ology of  the    debate.     While  some  particular  investigations  appear  to  show 

earth.  a  correSpOndence  for  a  time,  others  contradict  them.     If,  as  is 

not  antecedently  improbable,  some  real  connection  exists,  other 
disturbances  so  mask  and  distort  the  sun-spot  effects  that  the 
evidence  is  thus  far  inconclusive,  and  it  may  be  many  years 
before  the  question  can  be  finally  decided.  At  present  it  is  not 
certain  whether  the  earth  is  warmer  or  cooler,  more  rainy  or 
less  so,  at  the  time  of  sun-spot  maximum. 

It  is  certain  that  sun-spots  cannot  produce  any  sensible  effects 
by  their  direct  action  in  diminishing  the  heat  and  light  of  the 
sun,  since  they  never  cover  as  much  as  one-thousandth  part 
of  the  solar  surface.  There  seems  to  be,  however,  at  present, 
according  to  Halm,  a  slight  balance  of  statistical  evidence  in 
favor  of  the  belief  that  on  the  whole  the  temperature  of  the 
earth  is  really  slightly  higher  at  or  near  a  spot  minimum  than  at 
a  maximum. 


CHAPTER   IX 

THE    SUN  (Continued) 

The  Spectroscope,  the  Solar  Spectrum,  and  the  Chemical  Constitution  of  the  Sun— 
The  Doppler-Fizeau  Principle  —  The  Chromosphere  and  Prominences  —  The 
Corona  —  The  Sun's  Light — Measurement  of  the  Intensity  of  the  Sun's  Heat 
—  Theory  of  its  Maintenance  —  The  Age  and  Duration  of  the  Sun  —  Summary 
as  to  the  Constitution  of  the  Sun 

ABOUT  1860  the  spectroscope  appeared  in  the  field  as  a  new 
and  powerful  instrument  of  astronomical  research,  resolving  at 
a  glance  many  problems  which  before  had  seemed  to  be  abso- 
lutely inaccessible  to  investigation.  It  is  not  extravagant  to 
say  that  its  invention  has  done  almost  as  much  for  the  advance- 
ment of  astronomy  as  that  of  the  telescope. 

It  enables  us   to  study  the  light   that  comes  from  distant  Astronomi- 
obiects,  to  read  therein  a  record,  more  or  less  complete,  of  their  cal  imP°r- 

J  .   .  tance  of  the 

chemical  composition  and  physical  conditions,  to  measure  the  spectro- 
speed  with  which  they  are  moving  towards  or  from  us,  and  some-  sc°Pe- 
times,  as  in  the  case  of  the  solar  prominences,  to  see  and  observe 
at  any  time  objects  otherwise  visible  only  on  rare  occasions. 

244.   The  Spectroscope. — The  essential  part  of  the  instrument 
is  either  a  prism  or  train  of  prisms,  or  else  a  "  diffraction  grat-  The  essential 
ing,"  which  is  merely  a  piece  of  glass  or  speculum-metal,  ruled  ™e™ 
with  many  thousand  straight  equidistant  lines,  from  ten  thou-  scope: 
sand  to  twenty  thousand  in  each  inch.     Either  the  prism  or  the  the  Pri^m 
grating  performs  the  office  of  "  dispersing  "  the  rays  of  different 
wave-length  and  color. 

If  with  such  a  "dispersion  piece,"  as  it  may  be  called  (either 
prism  or  grating),  one  looks  at  a  distant  point  of  light, — a  star, 
for  instance, — he  will  see,  instead  of  a  point,  a  long  streak,  red 
at  one  end  and  violet  at  the  other.  If  the  object  observed  is 

217 


218 


MANUAL   OF   ASTRONOMY 


not  a  point,  but  a  line  of  light  parallel  to  the  edge  of  the  prism 
or  to  the  lines  of  the  grating,  then  instead  of  a  mere  colored 
streak  without  width  one  gets  a  spectrum,  —  a  colored  band  or 
ribbon  of  light, — which  may  show  transverse  markings  that 
will  give  the  observer  most  valuable  information. 

It  is  usual  to  form  this  line  of  light  by  admitting  the 
The  slit  and  light  through  a  narrow  slit  (seldom  more  than  -g-L-^  of  an  inch 
coihmator.  wj(je)  placed  at  one  end  of  a  tube  which  carries  at  the  other 


Prism  Spectroscope 


DirectrVision  Spectroscope 
FIG.  90.  —  Different  Forms  of  Spectroscope 

end  an  achromatic  object-glass  having  the  slit  in  its  principal 
focus  (Physics,  p.  318).  The  rays  from  the  slit  after  having 
passed  the  object-glass  form  a  parallel  beam,  just  as  if  they  had 
come  from  a  very  distant  object.  This  tube  with  slit  and  lens 
constitutes  the  collimator,  so  named  because  it  is  precisely  the 
same  as  the  instrument  used  with  the  transit-instrument  to 
adjust  its  line  of  collimation. 

Instead  of  looking  at  the  spectrum  with  the  naked  eye  it  is 
better  in  most  cases  to  magnify  it  by  using  a  small  view-telescope 


THE   SUN  219 

(so  called  to  distinguish  it  from  the  large  telescope  to  which  the 
spectroscope  is  often  attached). 

The  instrument,  therefore,  as  usually  constructed  and  shown 
in  the  diagram  (Fig.  90),  consists  of  three  parts,  —  collimator, 
prism  or  grating,  and  view-telescope,  —  although  in  the  "  direct- 
vision  "  spectroscope,  shown  in  the  figure,  the  view-telescope  is 
omitted. 

Fig.  91,  from  The  Sun,  by  permission  of  Appleton  &  Co.,  The  tele- 
represents  a  large  "  telespectroscope"  (as  the   combination  of  spec 
telescope  and  spectroscope  is  called)  arranged  for  photographic 
work. 

245.   The  Formation  of  the  Spectrum.  —  If  the  slit  S  be  illumi- 
nated by  strictly  "homogeneous  light"  (i.e.,  all  of  one  wave- 
length), a  single  image  of  it  will  be  formed.     If  the  light  is  How  the 
yellow,  a  yellow  image  will  appear  at  Y  (Fig.  90).     If  at  the 
same  time  light  of  a  different  wave-length  and  color  —  red,  for 
instance — be  also  admitted,  a  red  image  will  be  formed  at  R,  and 
the  observer  will  then  see  a  spectrum  with  two  bright  lines,  the 
lines  being  really  nothing  more  than  images  of  the  slit.     If  violet  The  spec- 
light  also  is  admitted,  a  third  (violet)  image  will  be  formed  at 
V,  and  the  spectrum  will  show  three  bright  lines.  the  slit. 

If  the  light  comes  from  a  luminous  solid,  like  the  lime  cylin- 
der of  a  calcium  light,  or  the  filament  of  an  incandescent  lamp, 
or  from  an  ordinary  gas  or  candle  flame  (in  which  the  light- 
giving  particles  are  really  bits  of  solid  carbon),  rays  of  all 
possible  wave-lengths  will  be  emitted  and  pass  through  the  slit,  The  con- 
and  as  a  consequence  we  shall  have  an  infinite  number  of  these  tmuous 

spectrum. 

slit-images  packed  close  together,  like  a  picket-fence  in  which 
the  pickets  touch  each  other  ;  we  then  get  what  is  called  a  con- 
tinuous spectrum,  ranging  in  color  from  red  at  one  end  to  violet 
at  the  other,  but  showing  no  transverse  lines  or  markings. 

If  the  light  comes,  however,  from  an  electric  discharge  between 
two  metallic  balls,  or  in  a  so-called  Geissler  tube,  or  from  a  Spectrum  of 
Bunsen-burner  flame  charged  with  the  vapor  of  some  volatile  brlght  lines' 


220 


MANUAL  OF  ASTRONOMY 


FIG.  91.  — Telespectroscope,  fitted  for  Photography 
From  The  Sun,  by  permission  of  the  publishers 


THE   SUN 


221 


metal,  the  spectrum  will  consist  of  a  series  of  bright  lines  or 
bands  of  different  colors  and  usually  numerous. 

246,   The   Solar   Spectrum.  —  If  we  look  at  sunlight,  either 
direct  or  reflected  (as  from  a  piece  of  paper  or  from  the  moon), 
we  get  a  spectrum,  continuous   in  the   main  but  crossed  by  The  solar 
thousands  of  dark  lines,  or  missing  slit-images,  known  as  the  8Pectrum 

y  and  its  dark 

"Fraunhofer  lines,     because  Fraunhofer  was  the  first  to  map  Fraunhofer 
them  (in  1814).     To  some  of  the  more  conspicuous  lines  he  lines- 
assigned  letters   of  the  alphabet  which  are   still  retained   as 
designations  :  thus,  A  is  a  strong  line  at  the  extreme  red  end  of 


FIG.  92.  —  H  and  K  Kegion  of  Solar  Spectrum 
From  photograph  by  Jewell,  Johns  Hopkins  University 

the  spectrum ;  C,  one  in  the  scarlet ;  D,  one  in  the  yellow ;  F, 
in  the  blue ;  and  H  and  K  are  a  pair  at  its  violet  extremity. 
Fig.  92  is  from  a  photograph  of  a  small  portion  of  the  violet 
region  of  the  solar  spectrum  including  the  great  H  and  K  lines. 
The  central  strip  is  made  by  light  from  the  very  edge  of  the 
sun;  the  strips  above  and  below,  by  light  from  the  center  of 
the  disk ;  there  are  some  notable  differences  in  the  appearance 
of  some  of  the  lines  in  the  two  cases. 

On  the  scale  of  the  lower  band  of  this  photograph  the  whole 
of  the  visible  part  of  the  solar  spectrum  would  be  about  20  feet 
long.  Our  present  maps  of  the  spectrum  contain  more  than  ten 


222 


MANUAL   OF   ASTRONOMY 


The  ultra- 
violet and 
infra-red 
invisible 
regions 
of  the 
spectrum. 


Position  of  a 
spectrum 
line  depends 
upon  the 
wave-length 
of  the  ray 
to  which  it 
is  due. 


Significance 
of  lines  in 
spectrum 
depends 
on  their 
arrange- 
ment and 
character- 
istics. 


Kirchhoff's 
laws. 


thousand  lines,  some  strong  and  heavy,  others  so  fine  as  to  be 
hardly  visible,  but  each  as  permanent  a  feature  of  the  spectrum 
as  rivers  and  cities  on  a  geographical  map. 

The  visible  portion  of  the  spectrum  is  by  no  means  the  whole, 
—  only  a  small  part  of  it,  indeed.  Above  H  and  K  lies  a  long 
"ultra-violet"  region  consisting  of  rays  whose  wave-length  is 
too  short  to  affect  our  eyes,  but  crowded  with  dark  lines  and 
accessible  to  photography.  At  the  other  end,  below  A,  there  is 
an  "  infra-red  "  region  some  twenty  times  as  long  as  the  visible 
spectrum  and  consisting  of  rays,  which,  while  they  bring  us 
a  large  part  of  all  the  heat  we  receive  from  the  sun,  have 
wave-lengths  too  long  to  produce  vision.  A  small  part  of  this 
infra-red  spectrum  can  be  photographed,  but  most  of  it  is 
accessible  only  to  such  heat-measuring  instruments  as  Lang- 
ley's  "bolometer"  (G-eneral  Astronomy,  Arts.  343  and  344). 
This  region  also  is  full  of  interspaces  of  exactly  the  same 
nature  as  the  dark  lines  in  the  visible  spectrum. 

The  position  of  each  line  in  the  spectrum  depends  entirely  on 
the  wave-length  or  luminous  pitch  of  the  ray  which  produces  it, 
or  rather  (since  the  line  is  dark)  has  been  suppressed,  and  is 
missing.  The  significance  of  the  lines  depends  upon  their 
arrangement  and  characteristics,  just  as  the  "sense"  of  a  printed 
page  lies  in  the  letters  and  their  grouping.  As  to  the  colors  of 
the  spectrum,  the  spectroscopist  generally  pays  no  more  attention 
to  them  than  the  geographer  to  the  colors  on  his  map. 

The  explanation  of  the  Fraunhofer  lines  remained  a  mystery 
for  nearly  fifty  years,  until  cleared  up  by  the  discoveries  of 
Kirchhoff  and  Bunsen  in  1859. 

247.   Principles   upon   which   Spectrum  Analysis  depends.  - 
These  (substantially),  as  announced  by  Kirchhoff  in  1859,  are 
the  three  following : 

(1)  A  Continuous  Spectrum  is  given  by  luminous  bodies, 
which  are  so  dense  that  the  molecules  interfere  with  each  other 
in  such  a  way  as  to  prevent  their  free  luminous  vibration,  i.e., 


THE   SUN 


223 


Screen 


Lime 


by  bodies  which  are  solid  or  liquid,  or,  if  gaseous,  are  under  high 
pressure.  Such  bodies  emit  a  jumble  of  all  possible  wave- 
lengths and  colors. 

(2)  The  spectrum  of  a  luminous  gas  under  low  pressure  is 
discontinuous,  made  up  of  bright  lines  or  bands,  and  these  lines 
are  characteristic ;  i.e.,  the  same  substance  under  similar  condi- 
tions always  gives  the  same  set  of  lines  and  generally  does  so 
even  under  conditions  considerably  different ;  but  it  may  (and 
many  gases  do)  give 

two  or  more  differ- 
ent spectra  when  the 
circumstances  differ 
too  widely. 

(3)  A  gas  or  vapor 
absorbs  from  a  beam 
of  white  light  which 
passes  through  it  pre- 
cisely   those    rays    of 
which,  when  the  gas  is 
luminous,  its  own  spec- 
trum   consists.      The 
spectrum  of  the  trans- 
mitted light  then 
exhibits   a  reversed 

spectrum,  which  shows  upon  a  continuous  background  dark 
lines  replacing  the  bright  ones  that  characterize  the  gas. 

This  principle  of  reversal  is  illustrated  by  Fig.  93.  In  front 
of  the  slit  of  the  spectroscope  is  placed  a  spirit-lamp  or  a 
Bunsen  burner,  with  a  little  bead  of  carbonate  of  soda  in  the 
flame,  and  if  we  add  a  little  salt  of  thallium,  we  shall  then  get 
a  spectrum  showing, the  two  principal  yellow  lines  of  sodium 
and  the  green  line  of  thallium,  —  all  three  bright.  If  now  a 
lime-light  or  an  electric  arc  be  put  in  action  behind  the  flame, 
we  at  once  get  the  effect  shown  at  the  bottom  of  the  figure,  — 


Origin  of  the 

continuous 

spectrum. 

Origin  of  the 
bright-lined 
spectrum. 


Absorbing 
power  pro- 
portional to 
radiating 
power. 


FIG.  93.  —Reversal  of  the  Spectrum 


Reversal  of 
lines  shown 
experimen- 
tally. 


224 


MANUAL   OF   ASTRONOMY 


Fraunhofer 
lines  due  to 
absorption 
of  rays  by 
the  atmos- 
pheres of 
the  sun  and 
earth. 


Determina- 
tion of 
elements 
existing  in 
the  solar 
atmosphere. 


Experi- 
mental 
arrange- 
ments. 


a  brilliant  continuous  spectrum  crossed  by  tbree  Hack1  lines 
which  exactly  replace  the  bright  ones.  Insert  a  screen  behind 
the  lamp  flame  and  the  lines  immediately  brighten  again. 

The  explanation  of  the  Fraunhofer  lines,  therefore,  is  that  they 
are  mainly  due  to  the  absorbing  action  of  the  gases  and  vapors  of 
the  solar  atmosphere  upon  the  light  transmitted  through  them  from 
the  liquid  or  solid  particles  which  compose  the  clouds  of  the  solar 
photosphere.  ^Some  of  the  dark  lines  of  the  solar  spectrum, 
known  as  telluric  lines,  are,  however,  due  to  the  gases  and 
vapors  of  the  earth's  atmosphere,  —  to  water  vapor  and  oxygen 
especially. 

248.  Chemical  Constituents  of  the  Sun.  — Numerous  lines  of 
the  solar  spectrum  have  been  identified  as  due  to  the  presence 
in  the  sun's  atmosphere  of  known  terrestrial  elements  in  the 
state  of  vapor. 

To  effect  the  comparison  necessary  for  this  purpose  the 
observer's  apparatus  must  be  so  arranged  that  he  can  confront 
the  spectrum  of  sunlight  with  that  of  the  substance  to  be 
examined,  which  must  be  brought  into  the  gaseous  condition,  so 
that  it  can  emit  its  characteristic  spectrum  of  bright  lines. 

In  the  case  of  those  substances  which  volatilize  at  a  compara- 
tively low  temperature,  as,  for  instance,  sodium,  calcium,  thal- 
lium, and  the  alkaline  metals  generally,  the  flame  of  a  spirit-lamp 
or  Bunsen  burner  answers  the  purpose.  A  little  piece  of  the 
metal  or  of  one  of  its  easily  volatilized  salts  is  inserted  in  the 
flame,  and  the  bright  lines  or  bands  of  its  spectrum  appear  at 
once  in  the  spectroscope. 

If  this  flame  is  not  hot  enough,  that  of  the  oxyhydrogen 
blowpipe  used  for  the  calcium  light  may  answer. 

1  Their  apparent  darkening,  however,  when  the  brilliant  light  from  the  lime 
is  transmitted  through  the  flame,  is  only  relative,  not  real.  Their  brightness  is 
actually  a  little  increased ;  but  the  brightness  of  the  background  is  increased 
immensely,  making  it  so  much  brighter  than  the  three  lines  that,  contrasted 
with  it,  they  look  black,  as  does  an  electric  arc  when  interposed  between  the 
eye  and  the  sun.  v  , 


THE   SUN 


225 


This  failing,  recourse  is  had  to  electricity.  Most  of  the 
metals  vaporize  at  once  in  the  electric  arc  between  carbon 
electrodes,  but  we  may  have  to  employ  the  still  higher  tem- 
perature of  an  electric  spark  produced  between 
electrodes  of  the  metal  by  an  "induction  coil"; 
and  in  passing  it  is  to  be  noted  that  the  spectrum 
of  the  metal  produced  by  the  spark  usually  pre- 
sents notable  differences  from  the  arc  spectrum. 

Finally,  if  we  have  a  permanent  gas,  say  hydro- 
gen, to  deal  with,  it  is  sealed  up,  usually  much 
rarefied,  in  a  glass  Geissler  tube  (Fig.  94),  5  or 
6  inches  long,  with  metallic  electrodes  at  each 
end,  by  means  of  which  electrical  discharges  can 
be  passed  through  the  gas. 

249.  Method  of  comparing  Spectra.  —  In  order 
to  effect  the  comparison,  half  the  slit  is  covered 
with  a  little  reflector,  or  a  so-called  "comparison 
prism"  which  reflects  into  it  the  sunlight,  while 
the  other  half  of  the  slit  receives  directly  the  light 
from  the  luminous  vapor.  Upon  looking  into 
the  spectroscope  the  observer  will  have  the  two 
spectra,  of  the  sunlight  and  of  the  metal,  side  by 
side,  and  can  at  once  see  what  bright  lines  of  the 
metallic  spectrum  do  or  do  not  exactly  coincide 
with  the  dark  lines  of  the  solar  spectrum.  If  he 
finds  that  every  one  of  the  conspicuous  bright 
lines  matches  a  conspicuous  dark  line,  he  can  be 
certain  that  the  substance  exists  as  vapor  in  the 
sun's  atmosphere. 

In  such  comparisons  photography  may  be  most  effectively 
used  instead  of  the  eye.  The  slit  of  the  spectroscope  is  so 
arranged  that  either  half  of  its  length  can  be  used  indepen- 
dently. An  impression  of  the  solar  spectrum  is  then  obtained 
by  a  few  seconds'  exposure  to  sunlight  admitted  through  one 


FIG.  94 
Geissler  Tube 


Volatiliza- 
tion of 
substances 
by  the  elec- 
tric arc 
and  spark. 


Elements 
detected  by 
the  coinci- 
dence of 
bright  lines 
in  their 
spectra  with 
Fraunhofer 
lines  in 
spectrum  of 
the  sun. 


Use  of 
photograph, 
in  making 
the  com- 
parison. 


226 


MANUAL   OF   ASTRONOMY 


half  of  the  slit,  which  is  then  closed,  and  the  room  darkened. 
Immediately  afterwards  light  from  an  electric  arc  containing 
the  vapor  of  metal  to  be  tested  is  admitted  through  the  other 
half  for  a  sufficient  time.  The  plate,  when  developed,  will  then 
show  the  two  spectra  side  by  side.  Fig.  95  is  a  half-tone  repro- 
duction, on  a  reduced  scale,  of  a  negative  made  by  Professor 
Trowbridge  in  investigating  the  presence  of  iron  in  the  sun. 
The  lower  half  is  part  of  the  violet  portion  of  the  sun's  spectrum 
(showing  dark  lines  as  bright),  and  the  upper  half  that  of  an  elec- 
tric arc  charged  with  the  vapor  of  iron.  In  the  original  every 
line  of  the  iron  spectrum  coincides  exactly  with  a  correlative  in 


FIG.  95 

the  solar  spectrum,  though  in  the  engraving  some  of  the  coinci- 
dences fail  to  be  obvious.  There  are,  of  course,  on  the  other 
hand,  certain  lines  in  the  solar  spectrum  which  do  not  find  any 
correlative  in  that  of  iron,  being  due  to  other  elements. 

250.  Elements  known  to  exist  in  the  Sun.  —  As  the  result  of 
such  comparisons,  first  made  by  Kirchhoff,  but  since  repeated 
and  greatly  extended  by  late  investigators,  a  large  number  of 
our  chemical  elements  have  been  ascertained  to  exist  in  the 
solar  atmosphere  in  the  form  of  vapor. 

Professor  Rowland  in  1890  gave  the  following  preliminary 
list  of  thirty-six  whose  presence  may  be  regarded  as  certainly 
established,  and  it  is  probable  that  further  research  will  add  a 
number  of  others.  The  elements  are  arranged  in  the  list  accord- 
ing to  the  intensity  of  the  dark  lines  by  which  they  are  repre- 
sented in  the  solar  spectrum ;  the  appended  figures  denote  the 


THE   SUN  227 

rank  which  each  element  would  hold  if  the  arrangement  had 
been  based  on  the  number  instead  of  the  intensity  of  the  lines. 
In  the  case  of  iron  the  number  exceeds  two  thousand. 


*  Calcium,  11. 

*  Strontium,  23. 

Copper,  30. 

*Iron,  i. 

*  Vanadium,  8. 

*  Zinc,  29. 

*  Hydrogen,  22. 

*  Barium,  24. 

*  Cadmium,  26. 

*  Sodium,  20. 

*  Carbon,  7. 

*  Cerium,  10. 

*  Nickel,  2. 

Scandium,  12. 

Glucinum,  33. 

*  Magnesium,  19. 

*  Yttrium,  15. 

Germanium,  3! 

*  Cobalt,  6. 

Zirconium,  9. 

Rhodium,  27. 

Silicon,  21. 

Molybdenum,  17. 

Silver,  31. 

Aluminium,  25. 

Lanthanum,  14. 

Tin,  34. 

*  Titanium,  3. 

Niobium,  16. 

Lead,  35. 

*  Chromium,  5. 

Palladium,  18. 

Erbium,  28. 

*  Manganese,  4. 

Neodymium,  13. 

Potassium,  36. 

An  asterisk  denotes  that  the  lines  of  the  element  indicated  appear  often  or 
always  as  bright  lines  in  the  spectrum  of  the  chromosphere  (Sec.  257). 

Helium  was  added  in  1895,  —  peculiar  in  that  it  manifests  its  Exceptional 
presence,  not  by  dark  Fraunhofer  lines,  but  only  by  bright  lines 
in  the  spectrum  of  the  chromosphere.     Certain  observations  of 
Runge  on  lines  in  the  infra-red  portion  of  the  spectrum  seem  to 
indicate  that  oxygen  should  also  be  included. 

It  will  be  noticed  that  all  the  bodies  named  in  the  list,  carbon 
and  hydrogen  alone  excepted,  are  metals,  and  that  many  of  the 
most  important  terrestrial  elements  fail  to  appear;  chlorine, 
bromine,  iodine,  sulphur,  phosphorus,  and  boron  are  all  missing, 
and  the  only  indications  of  the  presence  of  nitrogen  are  cyan- 
ogen bands  in  the  spectrum  of  sun  spots. 

251.   Unsafely  of  Negative  Conclusions.  — We  must  be  cautious,  Negative 
however,  in  drawing  negative  conclusions.     It  continually  hap-  Conclusions 
pens  that  when  a  mixture  of  gases  or  vapors  is  examined  with  ranted, 
the  spectroscope,  certain  ones  only  can  be  recognized;  as  long 
as  these  are  present  the  others  keep   in  hiding.      Thus  the 
presence  of  argon  in  atmospheric  air  cannot  be  detected  by  the 


228 


MANUAL  OF   ASTRONOMY 


Lockyer's 

dissociation 

theory. 


The  revers- 
ing layer. 


Reversal  of 
the  Fraun- 
hofer  lines 
at  the 
instant  of 
beginning 
or  end  of 
totality. 
The  flash 
spectrum. 


spectroscope  until  nearly  all  the  oxygen  and  nitrogen  have  been 
removed ;  and  the  other  new  gases  of  the  atmosphere,  krypton, 
neon,  and  xenon,  are  still  more  difficult  to  deal  with. 

It  is  quite  conceivable  also  that  the  spectra  of  the  missing 
elements  may  be,  under  solar  conditions,  so  different  from  their 
spectra  as  presented  in  our  laboratories  that  we  cannot  recognize 
them ;  for  it  is  now  unquestionable  that  many  substances  under 
different  conditions  give  two  or  more  widely  different  spectra, 
—  nitrogen,  for  instance. 

Lockyer  thinks  it  more  probable  that  the  missing  substances  are  not 
truly  "  elementary,"  but  are  decomposed  or  "  dissociated  "  by  intense  heat, 
and  so  cannot  exist  on  the  sun,  but  are  replaced  by  their  components. 
He  maintains,  in  fact,  that  none  of  our  so-called  "  elements  "  are  really 
elementary,  but  that  all  are  decomposable  and  are  to  some  extent  actually 
decomposed  in  the  sun  and  stars ;  and  some  of  them  by  the  electric  spark 
in  our  own  laboratories.  Granting  this,  many  interesting  and  remarkable 
spectroscopic  facts  find  easy  explanation.  At  the  same  time  the  hypothe- 
sis is  encumbered  with  serious  difficulties  and  has  not  yet  been  finally 
accepted  by  physicists  and  chemists. 

252.  The  Reversing  Layer.  —  According  to  Kirchhoff  s  theory, 
the  dark  lines  are  formed  by  the  transmission  of  light  emitted 
by  the  minute  solid  or  liquid  particles  of  which  the  photospheric 
clouds  are  supposed  to  be  formed,  through  somewhat  cooler 
vapors  containing  the  substances  which  we  recognize  in  the 
solar  spectrum.  If  this  be  so,  the  spectrum  of  the  gaseous 
envelope,  which  by  its  absorption  causes  the  dark  lines,  should 
by  itself  show  a  spectrum  of  corresponding  bright  lines. 

The  opportunities  are  rare  when  it  is  possible  to  obtain  the 
spectrum  of  this  gas  stratum  separate  from  that  of  the  photo- 
sphere ;  but  at  the  time  of  a  total  eclipse,  at  the  moment  when 
the  sun's  disk  has  just  been  obscured  by  the  moon  and  the 
sun's  atmosphere  is  still  visible  beyond  the  moon's  limb,  the 
observer  ought  to  get  this  bright  line  spectrum,  if  his  spectro- 
scope is  carefully  directed  to  the  exact  point  of  contact. 


THE  SUN  229 

The  actual  observation  was  first  made  during  the  Spanish 
eclipse  of  1870.  The  lines  of  the  solar  spectrum,  which  up  to 
the  time  of  the  final  obscuration  of  the  sun  had  remained  dark 
as  usual  (with  the  exception  of  a  few  belonging  to  the  spectrum 
of  the  chromosphere),  were  suddenly  reversed,  and  the  whole 
field  of  view  was  filled  with  brilliant  colored  lines,  which  flashed 
out  quickly  and  then  gradually  faded  away,  disappearing  in  two 
or  three  seconds, —  a  most  beautiful  thing  to  see. 

The  natural  interpretation  of  this  phenomenon  is  that  the 
dark  lines  in  the  solar  spectrum  are,  mainly  at  least,  produced 


K  H  H6  Hy 

FIG.  96.  —The  Flash  Spectrum 

by  a  very  thin  stratum  close  down  upon  the  photosphere,  since 
the  moon's  motion  in  three  seconds  would  cover  a  thickness 
of  only  about  800  miles.  It  was  not  possible,  however,  to  be 
certain  from  such  a  mere  glance  that  all  the  dark  lines  of  the 
solar  spectrum  were  reversed. 

Several  partial  confirmations  of  the  observation  have  since  been  visually 
obtained  at  eclipses,  though  none  so  complete  as  desirable ;  but  the  photo- 
graphs of  the  "  flash  spectrum,"  as  it  is  now  called,  obtained  during  the  Photo- 
recent  eclipses  of  1896,  1898,  1900,  and  1901,  made  with  various  forms  of  graphs  of 

the  "prismatic  camera"  (a  camera  of  long  focus,  with  a  prism,  a  train  as 

spectrum, 
of  prisms,  or  a  "  grating  "  outside  the  object-glass),  have  fully  corroborated 

it.  Fig.  96  is  a  reproduction  of  one  of  the  exquisite  photographs  of  the 
flash  spectrum  obtained  by  Sir  Norman  Lockyer  in  India  during  the  eclipse 


230 


MANUAL   OF   ASTRONOMY 


of  1898.  The  lines  above  (to  the  left  of  H  and  K)  are  in  the  invisible 
portion  of  the  spectrum  and  are  most  of  them  due  to  hydrogen.  Until 
these  permanent  records  of  the  phenomena  were  obtained  there  was  room 
to  doubt  whether  the  bright  lines  seen  might  not  belong  mainly  to  the 
spectrum  of  the  "chromosphere"  (Sec.  257),  instead  of  being  reversed 
Fraunhofer  lines. 

Sir  Norman  Lockyer  has  never  admitted  the  existence  of  any  such  thin 
"reversing  layer,"  maintaining  that  a  large  proportion  of  the  dark  lines 
are  formed  only  in  the  regions  of  lower  temperature,  high  up  in  the  sun's 
atmosphere,  and  not  close  to  the  photosphere,  i.e.,  different  lines  of  a  given 
substance  originate  at  very  different  elevations  in  the  solar  atmosphere. 

253.  Sun-Spot  Spectrum.  —  The  spectrum  of  a  sun-spot  differs 
from  the  general  solar  spectrum,  not  only  in  its  diminished 


FIG.  96  A.  —  Portion  of  Sun-Spot  Spectrum 
From  photograph  of  1893 

Peculiarities  brightness,  but  in  the  great  widening  and  intensification  of  cer- 

of  the  spec-    .^n  (jark  lines  and  the  thinning,  and  sometimes  the  reversal, 

sun-spot.        of  others,  especially  those  of  hydrogen  and  H  and  K  of  calcium, 

"the  great  twin  brothers,"  as  Miss  Clerke  calls  them,  which 

are  also  conspicuous  in  the  solar  prominences,   and,  we  may 

remark  in  passing,  are  also  always  reversed  in  the  spectrum  of 

the  faculse,  appearing  as  thin  bright  lines  running  through  the 

center  of  the  wide,  black,  hazy-edged  bands.     The  majority  of 

the  Fraunhofer  lines  are,  however,  as  a  rule,  quite  unaltered; 

and  in  the  case  of  those  substances  which  show  widened  lines 

in  the  spot  spectrum,  only  a  few  of  their  lines  are  thus  affected. 

Some  substances  which  are  very  inconspicuous  in  the  ordinary 

Vanadium      solar  spectrum  become  obtrusive  in  the  sun-spot  spectrum,  — 

in  sun-spots.  vanadium,  for  instance.     Fig.  96  A  is  from  a  photograph  of  the 


THE   SUN 


231 


yellowish-green  portion  of  a  sun-spot  spectrum  and  exhibits 
very  well  the  leading  characteristics. 

The  general  darkness  of  the  spectrum  of  a  sun-spot,  in  the 
green  portion  at  least,  appears  to  be  due  to  the  presence  of 
myriads  of  thin  dark  lines  so  closely  packed,  with  here  and 
there  an  interval,  as  to  be  resolvable  only  in  instruments  of  high 
power.  This  indicates  that  the  darkening  is  due,  in  part  at 
least,  to  the  absorption  of  light  by  transmission  through  vapors, 
rather  than  to  a  diminution  of  the  emissive  power  of  the  surface 
from  which  the  light  comes. 

254,  Displacement  and  Distortion  of  Lines.  —  Sometimes  in 
the  spectrum  of  an  active  sun-spot  or  of  a  prominence  certain 
lines  are  displaced  and  broken, 
as  shown  in  Fig.  97.  These 
distortions  can  be  explained  as 
due  to  the  swift  motion  towards 
or  from  the  observer  of  the 
gaseous  matter,  which  by  its 
absorption  produces  the  line 
observed.  .  In  the  case  illus- 
trated in  the  figure  hydrogen 

was  the  substance,  and  its  motion  was  away  from  the  earth  at 
the  rate  of  nearly  300  miles  a  second. 

The  general  principle  upon  which  the  explanation  of  such 
phenomena  depends  was  first  enunciated  by  the  German  physicist 
Doppler  in  1842,  and  has  turned  out  to  be  one  of  extreme 
importance  and  wide  application.  It  is  this :  When  the  distance 
between  the  observer  and  a  body  which  is  emitting  regular  vibra- 
tions is  increasing,  then  the  number  of  vibrations  received  in  a 
second  is  decreased  and  their  wave-length,  real  or  virtual,  is 
correspondingly  increased;  and  vice  versa  if  the  distance  is 
decreasing. 

Thus,  in  the  case  of  recession,  the  pitch  of  an  engine  whistle 
suddenly  drops  when  a  whistling  engine  passes  us  and  recedes; 


Darkening 
due  to 
absorption 
by  vapors. 


I 

, 

1 

J 

Displace- 
ment and 

' 

J 

1 

distortion 

If 

/ 

^ 

of  lines. 

\ 

i 

FIG.  97.  — The  C  Line  in  the  Spectrum  of 
a  Sun-Spot,  Sept.  22,  1870 


Doppler's 
principle. 


232 


MANUAL   OF   ASTRONOMY 


Effect  of 
motion  upon 
position  of 
lines  in  the 
spectrum. 
The  Dop- 
pler-Fizeau 
principle. 


Formula 
giving  rela- 
tion between 
the  radial 
velocity  of  a 
luminous 
object  and 
the  shift  of 
lines  in  its 
spectrum. 


and  a  light-ray  (say  the  particular  ray  which  produces  the  C  line 
in  the  spectrum  of  hydrogen)  has  its  wave-length  increased  and 
its  refrangibility,  which  depends  upon  its  wave-length,  dimin- 
ished, if  the  luminous  object  is  receding,  so  that  the  C  line  and 
all  the  other  hydrogen  lines  are  shifted  toward  the  red  end  of  the 
spectrum.  This  effect  of  motion  on  the  lines  of  the  spectrum 
was  first  pointed  out  by  Fizeau  in  1848,  so  that  in  its  astro- 
nomical application  the  principle  is  now  usually  referred  to  as 
the  "  Doppler-Fizeau  "  principle. 

Fig.  98  illustrates  the  principle.  The  lower  strip  is  a  small  piece  of  the 
yellow  portion  of  the  spectrum  of  a  star  (imaginary)  which  is  rapidly 
approaching  the  earth,  the  two  conspicuous  dark  lines  being  the  D1  and  D2 
lines  of  sodium.  The  upper  strip  is  the  corresponding  part  of  the  spectrum 

of  a  flame  or  electric  spark  con- 
taining sodium  vapor  and  show- 
ing its  lines  bright.  The  two 
spectra  are  confronted  by  a 
" comParison  prism"  (Sec.  249), 
and  it  is  obvious  that  the  lines 
of  the  star  spectrum  are  shifted 
towards  the  blue  end  by  about 

one  fourth  of  the  distance  between  the  D  lines,  i.e.,  by  about  1.5  units  of 
wave-length  on  the  Rowland  scale  (the  unit  is  one  ten-millionth  of  a  milli- 
meter). As  the  wave-length  of  D^  is  5896  units  (nearly),  it  follows  from 
the  formula  of  the  next  article  that  the  imaginary  star  must  have  been 
rushing  towards  us  at  the  rate  of  nearly  48  miles  a  second,  —  pretty  fast, 
but  several  real  stars  are  swifter. 

255.  Formula  of  the  Doppler-Fizeau  Principle.  —  While  the 
reasoning  upon  which  the  principle  rests  is  simple,  a  general 
theoretical  treatment  for  light-waves  is  difficult. 

For  the  demonstration  of  the  formulae  given  below,  the  reader 
is  referred  to  Frost's  translation  of  Schemer's  Astronomical 
Spectroscope/,  Part  II,  Chapter  II. 

If  V  is  the  velocity  of  light  (186330  miles  a  second),  r  the 
speed  with  which  the  observer  is  receding  from  the  object,  s 
the  speed  with  which  the  source  of  light  itself  is  receding,  A 


THE   SUN  233 

the  normal  wave-length  of  the  given  line  in  the  spectrum,  and 
X'  the  apparent  wave-length  as  affected  by  the  two  motions, 
we  have  the  equation  : 


Subtracting  X  from  both  sides  of  the  equation,  we  get 

V  -  X,  or  AX  =  \  2L±-!.,  (2) 

V  —  r 

which  holds  for  all  velocities,  great  or  small. 

Since,  however,  in  all  ordinary  cases  r  is  insignificant  as  com- 
pared with  F,  it  may  be  dropped  in  the  denominator,  and  we  have 


V 

Finally,  putting  v  for  r  +  «,  the  total  rate  at  which  the  distance 
between  the  object  and  the  observer  is  increasing,  we  have 

AX       v  AX 

_  =  -,  or,  =  FxT,  (3) 

which  is  the  usual  formula  employed  in  computing  "motion  in 
the  line  of  sight"  (or  "radial  velocity,"  as  it  is  now  usually 
called)  from  observations  of  the  shift  of  lines  in  the  spectrum. 
When  the  distance  is  decreasing,  v  becomes  negative,  and 
also  AX,  indicating  a  diminution  of  wave-length  and  a  cor- 
responding shifting  of  the  line  towards  the  blue  end  of  the 
spectrum.  At  present  motions  of  less  than  half  a  mile  per 
second  can  be  detected  by  the  spectroscopes  which  are  used  in 
studying  stellar  spectra. 

256.    Other  Causes  of  Displacement  of  Spectrum  Lines.  —  It  other  causes 
has  been  recently  (1895)  discovered  by  Humphreys  and  Mohler  whlchPr°- 
at  Baltimore  that  the  position  of  a  line  in  the  spectrum  of  a  somewhat 
luminous   vapor  may  also  be   shifted  in   a  somewhat  similar  similar 
manner    toivards   the   red  by  great   increase   of   pressure,  —  a  shift  of  lines 
pressure  of  180  pounds  to  the  square  inch  producing  as  great  inthe 
a  displacement  as  a  receding  rate  of  some  2  miles  a  second; 
but  the  shift  varies  for  different  lines  in  the  spectrum  and  does 
not  follow  the  same  law  as  in  the  case  of  motion. 


234  MANUAL   OF   ASTRONOMY 

In  1900  Professor  Julius  of  Utrecht  demonstrated  how  an 
apparent  shift  of  spectrum  lines  may  also  follow  from  what  is 
called  "anomalous  refraction"  in  the  sun's  atmosphere  near 
sun-spots  and  solar  prominences ;  and  Michelson  in  a  still  more 
recent  paper  shows  how  rapid  changes  of  density  in  the  medium 
through  which  light  comes  to  us  may  produce  similar  effects. 
It  is  quite  possible,  therefore,  that  some  of  the  phenomena  which 
have  hitherto  been  explained  on  the  Doppler-Fizeau  principle 
as  indicating  tremendous  velocities  of  moving  matter  may,  on 
further  examination,  receive  a  different  interpretation. 

257.   The  Chromosphere  and  Prominences.  —  Outside  the  pho^o- 
Thechromo-  sphere  lies  the  chromosphere,  of  which  the  lower  atmosphere,  or 
sphere.          "reversing  layer,"  is  only  the  densest  and  hottest  portion.    This 
chromosphere,  or  "  color  sphere,"  is  so  called  because  it  is  bril- 
liantly scarlet,  owing  the  color  to  hydrogen,  which  is  its  main, 
or  at  least  its  most  conspicuous,  constituent.     The  spectroscope 
shows  it  to  be  principally  composed  of  hydrogen,  helium,  and 
calcium  vapor.     In  structure  it  is  like  a  sheet  of  flame  over- 
lying the  surface  of  the  photosphere  to  a  depth  of  from  5000  to 
10000  miles,  and  as  seen  through  the  telescope  at  a  total  eclipse 
of  the  sun  has  been  aptly  described  as  like  "  a  prairie  on  fire."  l 
At  such  a  time,  after  the  sun  is  fairly  hidden  by  the  moon,  a 
number  of  scarlet  star-like  objects  are  usually  seen  blazing  like 
rubies  upon  the  contour  of  the  moon's  disk.    In  the  telescope  they 
look  like  fiery  clouds  of  varying  form  and  size,  and,  as  we  now 
know,  they  are  projections  from  the  chromosphere,  or  isolated 
The  promi-    clouds  of  chromospheric  material.    They  were  called  prominences 
nences  or       Qr  proiuoerances  as  a  sor^  of  non-committal  name,  while  it  was 

protuber- 
ances, still  uncertain  whether  they  were  appendages  of  the  sun  or  of 

the  moon. 

1  There  is,  however,  no  real  burning  in  the  case,  i.e.,  no  chemical  combina- 
tion going  on  between  the  hydrogen  and  some  other  element  like  oxygen.  The 
hydrogen  is  too  hot  to  burn  in  this  sense,  the  temperature  of  the  solar  surface 
being  above  that  of  dissociation, — so  high  that  any  compound  containing 
hydrogen  would  there  be  decomposed. 


THE   SUN 


235 


eous  con- 
stitution de- 
monstrated 
by  the  spec- 
troscope in 
1868. 


They  were  first  proved  to  be  solar  during  the  eclipse  of  1860, 
by  means  of  photographs  which  showed  that  the  moon's  disk 
moved  over  them  as  it  passed  across  the  sun.  Fig.  99  is  from 
a  photograph  of  the  eclipse  of  April,  1893,  by  Schaeberle. 

Their  real  nature  as  clouds  of  incandescent  gas  was  first 
revealed  by  the  spectroscope  in  1868,  during  the  Indian  eclipse  Their  gas- 
of  that  year.  On 
that  occasion  nu- 
merous observers 
recognized  in 
their  spectrum  the 
bright  lines  of  hy- 
drogen along  with 
another  conspicu- 
ous yellow  line, 
at  first  wrongly  at- 
tributed to  sodium 
but  afterwards  to 
a  hypothetical 
element  then  un- 
known in  our  lab- 
oratories and  pro- 
visionally named  FlG.  99.  _  Prominences,  1893 
"helium,"  its  yel- 
low line  being  known  as  D3  (Dx  and  D2  being  the  sodium  lines 
which  lie  close  by). 

Helium  was  discovered  as  a  terrestrial  element  in  April,  1895,  by  Dr.   The  identifi- 
Ramsay,  one  of  the  discoverers  of  argon.     In  examining  the  spectrum  of  cation  of 
the  gas  extracted  from  a  specimen  of  cleveite,  a  species  of  pitch-blende,  he 
found  the  characteristic  Dg  line  along  with  certain  other  unidentified  lines   eiement 
which  appear  in  the  spectrum  of  the  chromosphere  and  prominences.     The 
same  gas  has  since  been  found  in  a  number  of  other  minerals  and  mineral 
waters  and  also  in  meteoric  iron.     Its  density  turns  out  to  be  about  double 
that  of  hydrogen,  but  less  than  that  of  any  other  known  element,  and  it  resists 
liquefaction  more  stubbornly  tl^an  any  other  gas,  —  indeed,  it  is  the  only 


236 


MANUAL   OF   ASTRONOMY 


one  not  yet  subdued,  excepting  possibly  some  of  the  new  gases  (neon,  etc.) 
not  yet  obtained  in  sufficient  quantity  to  permit  investigation  on  this  line. 
Chemically,  it  is  extremely  inert,  refusing  to  enter  into  combination  with 
other  elements  (as  hydrogen  does  so  freely),  and  therefore  exists  on  the  earth 
only  in  minute  quantities.  It  seems,  however,  to  be  abundant  in  certain 
stars  and  nebulae,  where  its  lines  are  conspicuous  along  with  those  of 
hydrogen.  The  D3  line  is  not  the  only  helium  line,  but  the  chromosphere 
spectrum  contains  at  least  three  others  that  are  always  observable,  besides 
a  dozen  or  more  that  occasionally  make  their  appearance. 

The  II  and  K  lines  of  calcium  are  also,  like  those  of  hydrogen  and 
helium,  always  present  as  bright  lines  in  the  chromosphere ;  and  several 
hundred  lines  of  the  spectra  of  iron,  strontium,  magnesium,  sodium,  etc., 

have  been  observed  in  it  now 
and  then.  Fig.  100  shows  the 
appearance  of  the  calcium 
lines  in  the  chromosphere  spec- 
trum, and  also  the  hydrogen 
line  (He),  which  is  close  to 
the  II  line,  as  well  as  H£,  to 
the  left  of  K. 


Prominences 
observable 
with  the 
spectroscope 
without  an 
eclipse. 


H  and  He 


FIG.  100. — H  and  K  Lines  in  Chromosphere 
Spectrum 


258.  The  Prominences 
and  Chromosphere  obseAr- 
able  at  Any  Time  with 
the  Spectroscope.  —  Dur- 
ing the  eclipse  of  1868  Janssen  was  so  struck  with  the  bright- 
ness of  the  hydrogen  lines  in  the  spectrum  of  the  prominences 
that  he  believed  it  possible  to  observe  them  in  full  daylight,  and 
the  next  day  he  found  it  to  be  so.  He  also  found  that  by  a 
proper  management  of  his  instrument  he  could  make  out  the 
forms  and  structure  of  the  prominences  which  he  had  seen 
the  day  before  during  the  eclipse.  Lockyer,  in  England,  a  few 
days  later,  but  quite  independently,  made  the  same  discovery 
and  ascertained  that  the  prominences  were  mere  extensions 
from  a  hydrogen  envelope  completely  surrounding  the  sun,  and 
it  was  he  who  gave  to  this  envelope  the  now  familiar  name  of 
"chromosphere."  His  name  is  always,  and  justly,  associated 


THE   SUN 


237 


with  that  of  Janssen  as  a  co-discoverer.  A  little  later  Huggins 
showed  that  by  simply  opening  the  slit  of  the  spectroscope  the 
form  and  structure  of  the  prominence,  if  not  too  large,  could 
be  observed  as  a  whole,  and  not  merely  by  piecemeal  as  before. 
Within  the  last  few  years  it  has  become  possible  even  to  pho- 
tograph them  by  an  instrument  called  a  Spectroheliograph. 

259.  How  the  Spectroscope  enables  us  to  see  the  Chromosphere 
and  Prominences  without  an  Eclipse.  —  The  reason  why  we  can- 
not see  them  by  simply  screening  off  the  sun's  disk  is  that 
the  brilliant  illumination  of  our  own  atmosphere  near  the  sun 
drowns  them  out,  as  daylight  does  the  stars. 

When  we  point  the  telespectroscope  so  that  the  sun's  image 
falls  as  shown  in  Fig.  101,  with  its 
limb  just  tangent  to  the  edge  of  the 
slit,  then,  if  there  be  a  prominence  at 
that  point,  we  shall  get  two  overlying 
spectra:  one,  the  spectrum  of  the  illu- 
minated air  ;  the  other,  superposed  upon 
this  background,  is  that  of  the  promi- 
nence itself.  Now  the  latter  is  a  spec-  FlG- 101.  — Spectroscope  Slit 
trum  consisting  of  bright  lines,  or,  if 
the  slit  be  opened  a  little,  of  bright 
images  of  whatever  part  of  the  prominence  may  fall  between 
the  jaws  of  the  slit,  and  the  brightness  of  these  lines  or  images 
is  independent  of  the  dispersive  power  of  the  spectroscope; 
increase  of  dispersion  merely  sets  the  images  farther  apart,  with- 
out making  them  fainter  (except  as  light  is  lost  by  the  trans- 
mission through  a  greater  number  of  prisms).  The  spectrum  of 
the  aerial  illumination,  on  the  other  hand,  is  that  of  sunlight, — 
a  continuous  spectrum  showing  the  usual  Fraunhofer  lines ;  and 
this  spectrum  is  made  faint  by  great  dispersion.  Moreover,  it 
presents  dark  lines  or  spaces  just  at  the  very  places  in  the 
spectrum  where  the  bright  images  of  the  prominences  fall. 
They  therefore  become  easily  visible. 


Explana- 
tion of  the 
principle  by 
which  the 
spectroscope 
makes  the 
prominences 
visible.    It 
reduces  the 
brightness 
of  the  back- 
ground, but 
not  that  of 
the  promi- 
nences. 


adjusted    for    Observation 
of  the  Prominences 


238 


MANUAL   OF   ASTRONOMY 


A  grating  of  ordinary  power  attached  to  a  telescope  of  no  more  than 
2  or  3  inches  aperture  gives  a  very  satisfactory  view  of  these  beautiful 
and  interesting  objects.  The  red  image,  which  corresponds  to  the  C  line 
of  hydrogen,  is  by  far  the  best  for  visual  observations.  When  the  instru- 
ment is  properly  adjusted,  the  slit  slightly  opened,  and  the  image  of 
the  sun's  limb  brought  exactly  to  its  edge,  the  observer  at  the  eyepiece 
of  the  spectroscope  will  see  things  about  as  we  have  attempted  to  represent 
them  in  Fig.  102,  —  as  if  he  were  looking  at  the  clouds  in  an  evening  sky 
from  across  the  room  through  a  slightly  opened  window  blind. 

260.  Different  Kinds  of  Prominences.  —  The  prominences  may 
be  broadly  divided  into  two  classes,  — the  "  quiescent "  or  "  dif- 
fuse," and  the  "  eruptive"  or,  as  Secchi  calls  them,  the  "metal- 
lic," because  they  show  in 
their  spectrum  the  lines  of 
many  of  the  metals  in  addi- 
tion to  the  lines  of  hydrogen, 
helium,  and  calcium. 

The  Quiescent  Prominences 
are  immense  clouds,  often 
from  50000  to  100000  miles 
in  height  and  of  correspond- 
ing horizontal  dimensions, 
either  resting  directly  upon 
the  chromosphere  as  a  base, 
or  connected  with  it  by  stems 
and  columns,  as  shown  in 
Fig.  103  A,  though  in  some 
cases  they  appear  to  be  entirely  detached.  They  are  not  very 
brilliant  and  ordinarily  show  no  lines  in  their  spectrum  except 
those  of  hydrogen  and  helium  and  H  and  K  of  calcium  (which 
are  often  doubly  reversed,  as  shown  in  Fig.  100) ;  nor  are 
their  changes  usually  rapid,  but  they  often  continue  sensibly 
unaltered  sometimes  for  days  together,  i.e.,  as  long  as  they 
remain  in  sight  in  passing  around  the  limb  of  the  sun.  All 
their  forms  and  behavior  indicate  that,  like  the  clouds  in  our 


FIG.  102.  —  The  Chromosphere  and  Promi- 
nences seen  in  the  Spectroscope 


THE   SUN  239 

own  atmosphere,  they  exist,  and  float,  not  in  a  vacuum,  but  in 
a  medium  having  a  density  comparable  with  their  own,  though 
not  giving  bright  lines  in  its  spectrum,  and  for  that  reason  not 
visible  in  the  spectroscope.  They  are  found  on  all  portions  of 
the  sun's  disk,  not  being  confined  to  the  sun-spot  zones. 

The  Eruptive  Prominences,  on  the  other  hand,  appear  only  Eruptive,  or 
in  the  spot  zones,  and  as  a  rule  in  connection  with  active  spots.  metalllc» 

promi- 

Their  spectrum  usually  contains  the  bright  lines  of  various  nences 

metals,  magnesium  and  iron  being  especially  conspicuous,  and 

sodium   not   infrequent.     They   origi- 

nate  not  in  the  spots  themselves,  but 

in  the  disturbed  faculous  region  just 

outside.     Ordinarily  they  are  not  very 

large,    though  very  brilliant?   but   at 


Prominences,  Sept.  7, 1871, 12.30  P.M.  Same  at  1.15  P.M. 

FIG.  103.  —  A  Solar  Explosion 

times  they  become  enormous,  in  one  instance  under  the  writer's 

own  observation  reaching  an  elevation  of  more  than  400000 

miles.     They  are  most  fascinating  objects  to  watch,  on  account 

of  the  rapidity  of  their  changes.    Sometimes  the  actual  motion  of  Eapidity  of 

their  filaments  can  be  perceived  directly,  like  that  of  the  minute-  chanse- 

hand  of  a  clock,  and  this  implies  a  velocity  of  at  least  250  miles 

a  second  in  the  moving  mass.     In  such  cases  the  lines  of  the 

spectrum  are  also,  of  course,  greatly  displaced  and  distorted. 

Fig.  103  represents  a  prominence  of  this  sort  at  two  times,  separated  by 
an  interval  of  three  quarters  of  an  hour.     The  large  quiescent  prominence 


240 


MANUAL   OF   ASTRONOMY 


Solar 
explosions. 


of  Fig.  A  was  completely  blown  to  pieces,  as  shown  in  J3,  by  the  "  explo- 
sion," as  it  may  be  fairly  called,  which  occurred  beneath  it, — the  first  case  in 
which  such  a  phenomenon  was  actually  observed.  See  also  Fig.  104,  show- 
ing successive  stages  of  an  eruptive  prominence  photographed  at  Professor 
Hale's  private  observatory  in  1895.  A  considerable  number  of  similar 
occurrences  have  been  recorded  by  various  observers  during  the  last  thirty 
years,  but  they  are  by  no  means  every-day  affairs. 

The  number  of  prominences  of  both  kinds  visible  at  one  time  on  the 
circumference  of  the  sun's  disk  ranges  from  one  or  two  to  twenty-five  or 
thirty ;  the  eruptive  prominences  being  numerous  only  near  the  times  of 
sun-spot  maximum. 

261.    Photography  of  Prominences ;  the  Spectroheliograph.  — 
It  is  possible^  but  not  very  satisfactory,  to  photograph  a  small 

prominences  \ J  J  r  °     r 

by  simple 
spectro- 
scope. 


Number 
of  promi- 
nences. 


Photog- 
raphy of 


Photog- 
raphy by 
the  spectre- 
heliograph. 


10.34  10.40 

FIG.  104.  —Photographs  of  Prominences,  March  25,  1895 
After  Hale 

prominence  by  the  same  arrangement  as  for  visual  observation, 
merely  putting  a  sensitive  plate  at  the  focus  of  the  "  view- 
telescope  "  (Sec.  244),  using  the  F  line  of  the  spectrum,  or, 
better,  the  K  line,  instead  of  the  red  C. 

A  much  better  plan  is  to  use  a  "  spectroheliograph,"  -  inde- 
pendently devised  by  Professor  Hale  of  Chicago  and  Deslandres 
of  Paris.  A  detailed  description  would  take  too  much  space, 
but  the  essential  feature  is  a  narrow  slit  moving  in  front  of  the 
sensitive  plate  in  exact  accordance  with  the  motion  of  the 


THE   SUN 


241 


collimator  slit ;  so  that  as  the  latter  is  moved  across  the  image  of 
the  prominence,  while  the  former  moves  before  the  plate,  the 
bright  K  line  of  each  portion  of  the  prominence  shines  through 
upon  the  plate  and  so  photographs  the  object  in  sections,  by  its 
"K-light,"  if  the  ex- 
pression may  be 
allowed. 

Fig.  104  is  from  a  nega- 
tive thus  made  at  Pro- 
fessor Hale's  private 
Kenwood  observatory  on 
March  25,  1895,  with 
the  then  newly  invented 
spectroheliograph,  —  three 
exposures  on  an  ascend- 
ing prominence  at  inter- 
vals of  six  and  eighteen 
minutes.  During  this  time 
the  height  of  the  promi- 
nence increased  from 
135000  miles  to  281000. 
Fig.  104  A  exhibits  the 
whole  sun  with  its  spots 

and  faculae  and  the  surrounding  chromosphere,  —  made  by  the  same  in- 
strument. A  screen  covers  the  sun's  image  while  the  chromosphere  and 
prominences  are  first  photographed  by  a  slow  motion  of  the  slit,  and  then, 
the  screen  being  removed,  the  slit  is  drawn  back  rapidly  across  the  sun's 
image,  thus  producing  the  picture  of  the  solar  surface. 

262.   The  Corona. —  The  corona  is  a  halo  or  glory  of  light  which  The  corona: 
surrounds  the  sun  at  the  time  of  a  total  eclipse  and  has  been  its  seneral 
known  from  remote  antiquity  as  one  of  the  most  beautiful  and 
impressive  of  all  natural  phenomena.     The  portion  near  the 
sun  is  dazzlingly  bright  and  of  a  pearly  tinge,  which  contrasts 
finely  with  the  scarlet  prominences.     It  is  made  up  of  filaments 
and  rays  which,  roughly  speaking,   diverge    radially,  but  are 
strangely  curved  and  intertwined.     At  a  little  distance  from 


FIG.  104  A.  —  Spectroheliogram  of  Entire  Sun 
After  Hale 


appearance. 


242 


MANUAL   OF   ASTRONOMY 


the  edge  of  the  sun  the  light  becomes  more  diffuse,  and  the 
outer  boundary  of  the  corona  is  not  very  well  denned,  though 
certain  dark  rifts  extend  through  it  clear  to  the  sun's  surface. 

Often  the  filaments  are  longest  in  the  sun-spot  zones,  giving 
the  corona  a  roughly  quadrangular  form.     This  seems  to  be 


FIG.  105.  — Corona  of  1871 

specially  the  case  in  eclipses  which  occur  near  the  time  of  a 
sun-spot  maximum.  In  eclipses  which  occur  near  the  sun-spot 
minimum,  on  the  other  hand,  the  equatorial  rays  predominate, 
forming  streamers,  sometimes  fan-like  and  sometimes  pointed, 
extending  several  millions  of  miles  from  the  solar  surface. 
Near  the  poles  of  the  sun  there  are  usually  tufts  of  sharply 
defined  threads  of  light,  which  curve  both  ways  from  the  pole. 


THE   SUN 


243 


The  corona  varies  greatly  in  brightness  at  different  eclipses,  Light  given 
according  to  the  apparent  diameter  of  the  moon  at  the  time,  bythe 

corona. 

and  with  the  sun-spot  period.     Its  total  light  is  always  at  least 
two  or  three  times  as  great  as  that  of  the  full  moon. 

Drawings  and  Photographs  of  the  Corona.  —  There  is  very  great  diffi-  Drawings 
culty  in  getting  accurate  representations  of  this  phenomenon.     The  two   anc*  Pnot°- 
or  three  minutes  during  which  only  it  is  usually  visible  at  any  given   grap 
eclipse  do  not  allow  time  for  trustworthy  hand-work ;  at  any  rate,  draw- 
ings of  the  same  corona  made  even  by  good  artists,  sitting  side  by  side, 


FIG.  106.  —  Corona  of  Eclipse  of  1900,  Wadesboro,  N.C. 

differ  very  much,  —  sometimes  ridiculously.  Photographs  are  better,  so 
far  as  they  go,  but  hitherto  they  have  not  succeeded  in  bringing  out 
many  details  of  the  phenomenon  which  are  easily  visible  to  the  eye ;  nor 
do  the  pictures  which  show  well  the  outer  portions  of  the  corona  generally 
bring  out  the  details  near  the  sun's  limb,  though  an  ingenious  device  of 
Burckhalter,  which,  by  a  whirling  screen  of  peculiar  form  in  front  of  the 
sensitive  plate,  gives  a  much  longer  exposure  to  the  outer  regions  than  to 
the  parts  near  the  sun,  has  greatly  improved  the  results. 

Fig.  105  is  copied  from  an  engraving  made  by  combining  several  photo- 
graphs of  the  eclipse  of  1871.  Fig.  106  is  reduced  from  a  drawing 
Dy  Wesley  of  the  corona  of  the  eclipse  of  May,  1900,  made  from  a 


244 


MANUAL   OF   ASTRONOMY 


The  spec- 
trum of  the 
corona.   The 
green  line, 
X=5304. 


Coronium 
probably  a 
gas  of  ex- 
tremely low 
density. 


combination  of  the  sketches  and  photographs  obtained  by  the  members  of 
the  various  eclipse  parties  of  the  British  Astronomical  Association.  It  is 
an  admirable  representation  of  what  the  writer  saw  at  Wadesboro,  N.C., 
except  that  the  curved  wings  on  the  west  and  the  long,  pointed,  eastern 
streamer  could  all  be  traced  much  farther  by  the  eye,  —  to  a  distance  fully 
three  and  a  half  times  the  moon's  diameter,  or  at  least  3  000000  miles. 

263,  Spectrum  of  the  Corona.  —  The  characteristic  feature  of 
the  visual  spectrum  is  a  bright  green  line  which  lies  very  near, 
and  was  long  supposed  to  be  the  "  reversal  "of,  a  dark  line  in 
the  solar  spectrum,  —  known  as  the  "  1474  line,"  because  its 
position  is  at  1474  on  the  scale  of  KirchhofFs  map  of  the  spec- 
trum, generally  used  in  1869,  when  the  corona  line  was  first 
discovered.  This  identification,  for  which  the  writer  was 
mainly  responsible,  turns  out,  however,  to  be  erroneous,  the 
wave-length  of  "  1474  "  being  about  5317  on  Rowland's  scale, 
while  the  wave-length  of  the  real  corona  line,  as  first  discovered 
from  the  photographs  in  1898  (and  since  confirmed),  is  5304. 

The  "  1474 "  line  (probably  of  iron)  is  always  present  in 
the  chromosphere  spectrum  as  a  bright  line,  and  at  an  eclipse 
when  the  corona  first  appears  it  is  much  the  brightest  line  in 
the  green  part  of  the  spectrum ;  but,  as  we  now  know,  it  fades 
out  shortly,  while  the  true  corona  line,  which  is  much  fainter, 
remains,  of  course,  visible  through  the  whole  totality. 

The  unknown  substance  which  produces  this  corona  line  has 
been  provisionally  named  "coronium,"  just  as  "helium"  was 
named  twenty-seven  years  before  it  was  identified  as  a  terres- 
trial element.  It  is  probably  a  gas  of  extremely  low  density,  — 
perhaps  even  lighter  than  hydrogen. 

Besides  this  conspicuous  green  line  there  are  several  others, 
—  five  at  least  and  probably  more,  —  all  in  the  violet  or  ultra- 
violet, all  probably  due  to  the  same  substance,  and  showing, 
like  the  principal  line,  but  much  more  faintly,  as  rings  on 
photographs  made  by  the  prismatic  camera  during  the  recent 
eclipses. 


THE   SUN  245 

The  hydrogen  and  helium  lines,  and  H  and  K  of  calcium,  Hydrogen 
have  also  been  photographed  as  bright  lines  during  eclipses  and  ^f^^n 
attributed  to  the  corona;  the  later  observations  prove,  however,  the  corona, 
that  they  are  not  really  coronal,  but  are  due  to  reflection  (in  our 
own  atmosphere)  of  light  coming  from  the  chromosphere  and 
prominences. 

The  light  of  the  corona  is  distinctly  polarized :   on  one  or  Part  of  the 
two  occasions  observers  have  also  reported  in  its  visual  spec-  hghtofthe 

r  ^  corona  due 

trum  the  presence  of  dark  Fraunhof er  lines,  and  these  have  now  to  reflection, 
at  last  been  successfully  photographed  by  the  Lick  observers 
during  the   Sumatra  eclipse  of  1901.      The   corona  therefore 
unquestionably  contains  some  matter  which  reflects  sunlight. 

264.  Nature  of  the  Corona.  —  The  corona  is  proved  to  be  a  The  corona 
true  solar  appendage  and  not  a  mere  optical  phenomenon,  nor 
due  to  either  the  atmosphere  of  the  earth  or  moon,  by  two 
unquestionable  facts :  first,  its  spectrum  as  described  above  is 
not  that  of  mere  reflected  sunlight,  but  of  a  glowing  gas; 
and  second,  photographs  of  the  corona  made  at  widely  different 
stations  on  the  track  of  an  eclipse  show,  in  the  main,  details 
that  are  identical  as  seen  at  stations  thousands  of  miles  apart, 
and  exhibit  the  motion  of  the  moon  across  the  coronal  filaments. 
In  a  sense,  then,  the  corona  is  a  phenomenon  of  the  sun's 
atmosphere,  though  this  solar  "atmosphere"  is  very  far  from  Not  related 
bearing:  to  the  sun  the  same  relations  that  are  borne  towards  the  to  the  sun 

as  our  own 

earth  by  the  air.     The  corona  is  not  a  simple  spherical  envelope  atmosphere 
of  gas  comparatively  at  rest  and  held  in  equilibrium  by  gravity,  1S  related  to 
but  other  forces  than  gravity  are  dominant  in  it,  and  matter 
that  is  not  gaseous  probably  abounds. 

Its  phenomena  are  not  yet  satisfactorily  explained  and  remind  Specula- 
us  far  more  of  auroral  streamers  and  comets'  tails  than  of  any-  !lons  f s  to 

J      its  nature 

thing   that   occurs   in   the   lower    regions   of    our   terrestrial  and  the 
atmosphere.     Indeed,  there  are  many  features  which  warrant  f orces  whlch 

.      .  determine 

something  more  than  a  mere  suspicion  that  it  is  more  or  less  its  form, 
analogous  to  Roentgen  and   cathode   rays,  due,  as  Professor 


246 


MANUAL   OF   ASTRONOMY 


Bigelow  suggests,  to  ions  driven  off  from  the  molecules  of  the 
solar  gases  and  controlled  in  their  motions  by  electric  and 
magnetic  forces  emanating  from  the  sun.  (See  also  Sec.  502.) 
That  the  corona  is  composed  of  matter  excessively  rarefied 
is  shown  by  the  fact  that  in  a  number  of  cases  comets  are 
known  to  have  passed  directly  through  it  (as,  for  instance,  in 
1882)  without  the  slightest  perceptible  disturbance  or  retarda- 
tion of  their  motion.  Its  mean  density  must,  therefore,  be 
almost  inconceivably  less  than  that  of  the  best  vacuum  we  are 
able  to  make  by  artificial  means. 

Numerous  attempts  have  been  made  to  find  a  way  of  observing  the 
corona  without  an  eclipse,  but  thus  far  without  any  certain  result.  The 
spectroscopic  method,  which  succeeds  with  the  chromosphere  and  promi- 
nences, fails  with  the  corona,  because  the  lines  of  its  spectrum  are  not 
bright  enough ;  and,  moreover,  there  are,  in  the  ordinary  solar  spectrum,  no 
dark  lines  to  match  them  and  help  in  forming  a  background.  Further- 
more, since  the  streamers  of  the  corona  are  probably  not  entirely  gaseous, 
but  partly  of  dust-like  constitution  (giving,  therefore,  the  spectrum  of 
reflected  sunlight),  they  at  least  would  not  be  observable  by  this  method. 


THE  SUN'S  LIGHT  AND  HEAT 

265.  The  Sun's  Light. — By  photometric  methods  (Physics, 
p.  328)  we  can  compare  the  sun's  light  with  that  of  a  "  standard 
candle  "  (Physics,  p.  277),  and  we  find  that  the  sun  gives  us 
1575  billions  of  billions  (1575  X  1024)  times  as  much  light  as  a 
standard  candle  would  give  at  that  distance. 

Experiment  shows  that  when  the  sun  is  overhead  sunlight 
illuminates  a  white  surface  about  65000  times  as  brightly  as  a 
standard  candle  at  one  meter  distance,  or  certainly  not  less  than 
70000  times,  if  we  allow  for  the  absorption  of  sunlight  in  our 
air.  Multiplying  this  70000  by  the  square  of  the  sun's  distance 
in  meters  (15  x  1010)2,  we  get  the  sun's  "candle-power"  as 
stated  above.  But  the  determination  cannot  claim  any  minute 
accuracy,  because  of  the  continual  variations  in  the  purity  of 


THE   SUN  247 

our  atmosphere  and  the  difficulty  in  determining  the  losses  of 
the  sunlight  before  it  reaches  the  photometric  screen. 

The  light  received  from  the  sun  is  about  600000  times  that  Sunlight 
of   the  moon,   about    7000000000    times  that   of.Sirius,   the  ^Jrt 
brightest  of  the  fixed  stars,  and  about  50000  000000  times  that  from  other 
of  Vega  or  Arcturus.  bodies> 

The  intensity  of  sunlight  is  the  amount  of  light  emitted  by 
each  square  unit  of  its  surface,  —  a  very  different  matter  from 
its  total  quantity.     From  the  best  data  at  present  obtainable 
(only   rather   rough    approximations    are    possible)    the    sun's 
surface   appears    to    be    about    190000    times    as    bright   as    a  intensity  of 
candle  flame,  and  about  150   times  as  bright  as  the  calcium  sunlisht- 
light.     The  brightest  part  of  the  electric  arc-light  —  its  "  crater" 
—  comes    nearer   to    the    brilliance    of  the  solar  surface  than 
anything  else  we  know  of,  being  from  one  half  to  one  fourth  as 
bright. 

266.    Relative    Brightness   of   Different   Parts   of  the    Sun's 
Disk.  —  As  already  stated  (Sec.  233),  the  sun's  disk  is  brightest 
at  the  center,  but  the  variation  is  very  slight  until  near  the  Darkening 
edge,  where  the  brightness  falls  off  very  rapidly,  so  that  at  the  JjJSSra* 
limb  itself  it  is  not  more  than  one  third  of  the  brightness  at  andmodi- 
the  center.     The  color  is  modified  also,  verging  towards  choco-  ficatlon 

of  color. 

late,  because  the  blue  and  violet  rays  are  much  more  affected 
than  the  red  and  yellow ;  this  is  the  reason  why  the  darkening 
at  the  limb  of  the  sun  is  so  much  more  conspicuous  in  the 
photographs  than  in  the  telescope. 

The  darkening  is  unquestionably  due  to  the  general  absorp- 
tion of  light  by  the  lower  parts  of  the  sun's  atmosphere,  though  The  sun 
it  is  difficult  to  determine  iust  how  much  the  sun's  brightness  8triPPed  of 

J  °  its  atmos- 

is  diminished  by  it.     Different  estimates  vary  considerably,  but  phere 
according  to  Langley,  if  the  sun's  atmosphere  were  removed,  we  would  be 

,        , ,  -  ,     blue  and 

should  receive  from  two  to  five  times  as  much  light  as  now,  and,  much  more 
moreover,  its  tint  would  be  strongly  blue,  more  blue  even  than  brilliant, 
that  of  an  electric  arc. 


248 


MANUAL  OF  ASTRONOMY 


The  sun's 
heat:  its 
quantity" 
expressed 
in  calories. 
The  solar 
constant. 


The  engi- 
neer's 
calory 
and  the 
small  calory, 
or  calorette. 


Values 
obtained  for 
the  solar 
constant 
range  from 
19  to  40. 

Method  of 
determining 
the  solar 
constant. 


267.  The  Quantity  of  Solar  Heat ;  the  Solar  Constant.  —  The 

solar  constant  is  the  number  of  heat-units  which  a  square  unit  of 
the  earths  surface,  unprotected  by  any  atmosphere,  and  exposed 
perpendicularly  to  the  sun's  rays, .  would  receive  in  a  unit  of  time. 
(Recent  results  obtained  by  the  Smithsonian  observers  seem  to 
indicate  that  this  quantity  is  not  really  a  "constant,"  but  is 
subject  to  fluctuations  of  from  three  to  five  per  cent.)  The  heat- 
unit  most  used  at  present,  by  engineers  at  least,  is  the  calory, 
which  is  the  amount  of  heat  required  to  raise  the  temperature 
of  one  kilogram  of  water  1°  C.  A  smaller  unit,  only  ^QQ  part 
as  great,  is  much  used  in  scientific  work,  substituting  in  the 
definition  a  gram  of  water  for  the  kilogram.  This  heat-unit  is 
called  the  "  small  calory,"  -  it  might  perhaps  be  named  'the 
"  calorette." 

As  the  result  of  the  best  observations  thus  far  made,  it  is  found 
that  the  solar  constant  is  about  nineteen  and  one-half  engineer  s 
calories  per  square  meter  per  minute,  or  1.95  "  calorettes "  per 
square  centimeter  per  minute.1 

In  what  follows  we  have  used  21  as  the  solar  constant, 
although  this  seems  now  a  little  too  high.  The  different  deter- 
minations, since  that  first  made  by  Pouillet  and  Herschel  in 
1838,  range  all  the  way  from  19  to  40,  —  an  indication  of  the 
extreme  difficulty  of  the  subject.  At  the  earth's  surface  a  square 
meter  seldom  actually  receives  more  than  fifteen  calories  in  a 
minute,  fully  fifty  per  cent  being  lost,  or  diverted,  in  its  passage 
through  the  atmosphere. 

268.  Method  of  determining  the  Solar  Constant.  —  The  princi- 
ple is  simple,  though  the  practical  difficulties  are  very  great, 
and  so  far  have  prevented  any  high  degree  of  accuracy. 

The  determination  is  made  by  admitting  a  beam  of  sunlight,  of 

1  There  would  be  some  advantage  in  stating  the  solar  constant  on  the  C.G.So 
system,  by  dividing  2.0  by  60,  the  number  of  seconds  in  a  minute.  According 
to  this,  the  solar  constant  equals  0.032  C.G.S.,  or  -^  of  a  "calorette,"  received 
on  a  square  centimeter  in  one  second. 


THE  SUN  249 

known  cross-section,  to  fall  upon  a  known  quantity  of  water,  for 
a  known  time,  and  measuring  the  consequent  rise  of  temperature. 

It  is  necessary,  however,  to  determine  and  allow  for  all  heat 
lost  by  the  apparatus  during  the  experiment  or  received  from 
other  sources,  and  especially  to  take  into  account  the  effect  of 
atmospheric  absorption.     This  is  the  most  difficult  and  uncer-  Difficulties 
tain  part  of  the  operation,  since  the  absorption  is  continually  and  uncer- 

J    tainties. 

changing,  —  capriciously  with  the  meteorological  conditions,  and 
regularly  with  the  changing  altitude  of  the  sun. 

It  should  be  noted  that  the  rays  absorbed  by  the  atmosphere, 
though  diverted  from  the  instrument  which  is  endeavoring  to 
measure  their  amount,  are  not  lost  to  the  earth.  The  air  is 
illuminated  and  warmed  by  them,  and  the  earth  gets  the  bene- 
fit of  the  effect  at  second  hand,  so  to  speak. 

For  a  description  of  the  pyrheliometer  and  actinometer,  with  which  the 
heat  radiation  is  measured,  and  of  the  bolometer,  with  which  the  percent- 
age of  loss  is  determined  for  rays  of  differing  wave-length,  the  student  is 
referred  to  the  General  Astronomy,  Arts.  340-345. 

269.  The  Solar  Heat  at  the  Earth's  Surface  expressed  in  Terms  Solar  heat 
of  Melting  Ice. — Since  it  requires  79£  calories  of  heat  to  melt  ^pressed  in 
a  kilogram  of  ice  with  a  specific  gravity  of  0.92,  it  follows  that,  melting  ice. 
taking  the  solar  constant  at  21,  the  heat  received  from  a  verti- 
cal sun  would  melt  in  an  hour  a  sheet  of  ice  17.3  millimeters, 

or  seven-tenths  of  an  inch  thick.  From  this  it  is  easily  com- 
puted that  the  amount  of  heat  received  by  the  earth  from  the 
sun  in  a  year  is  sufficient  to  melt  a  shell  of  ice  160  feet  thick  on 
the  earth's  equator,  or  124  feet  over  the  earth's  entire  surface, 
if  the  heat  were  equally  distributed  over  all  latitudes. 

270.  Solar  Heat  expressed  as  Energy.  —  Since  according  to  Expressed 
the   known   value    of   the    "mechanical   equivalent  of   heat"  as  energy 
(Physics,  p.  260)  a  horse-power  (33000  foot-pounds  per  minute)  horse. 
can  easily  be  shown  to  be  equivalent  to  about  10.7  calories  per  power, 
minute,  it  follows  that  each  square  meter  of  the  earth's  surface 


250 


MANUAL   OP   ASTRONOMY 


The  solar 
engine. 


Solar  radi- 
ation at 
the  sun's 
surface. 


perpendicular  to  the  sun's  rays  ought  to  receive  about  2.0  horse- 
power continuously.  Atmospheric  absorption  cuts  this  down  to 
about  1J  horse-power,  of  which  about  one  eighth  can  be  realized 
by  a  suitable  machine,  such  as  Ericsson's  solar  engine  (Fig.  107), 
which  for  several  years  was  exhibited  annually  in  New  York. 

The  solar  heat  was  concentrated  by  the  large  reflector,  18  feet  in  diame- 
ter, upon  the  boiler,  which  was  a  6-inch  iron  tube.  A  "  head  "  at  the  upper 
end  (removed  when  the  photograph  was  taken)  received  the  steam,  and  a 

pipe  connected  it  with 
the  4 -horse-power  en- 
gine shown  under- 
neath. When  the  sun 
shone  it  worked  well. 

The  energy  an- 
nually  received 
from  the  sun  by  the 
whole  of  the  earth's 
surface  aggregates 
nearly  70  mile- 
tons  to  each  square 
foot.  That  is,  the 
average  amount  of 
heat  annually  re- 
ceived by  each 
square  foot  of  the 
earth's  surface,  if  utilized  in  a  theoretically  perfect  heat  engine, 
would  hoist  nearly  70  tons  to  the  height  of  a  mile. 

271.  Solar  Radiation  at  the  Sun's  Surface.  —  If  now  we  esti- 
mate the  amount  of  radiation  at  the  sun's  surface  itself,  we 
come  to  results  which  are  simply  amazing.  We  must  multiply 
the  solar  constant  observed  at  the  earth  by  the  square  of  the 
ratio  between  93  000000  miles  (the  earth's  distance  from  the 
sun)  and  433250  (the  radius  of  the  sun).  This  square  is  about 
46000.  In  other  words,  the  amount  of  heat  emitted  in  a  minute 


FIG.  107.  — Ericsson's  Solar  Engine 


THE   SUN  251 

by  a  square  meter  of  the  sun's  surface  is  about  46000  times  as 

great  as  that  received  by  a  square  meter  at  the  earth.     Carrying 

out  the  figures,  we  find  that  this  heat  radiation  at  the  sun's 

surface    amounts    to    1 000000   calories  per    square  meter  per 

minute;  that  if  the  sun  were  frozen  over  completely,  to  a  depth  of 

45  feet,  the  heat  emitted  would  melt  the  shell  in  one  minute;  Expressed 

that  if  a  bridge  of  ice  could  be  formed  from  the  earth  to  the  m  ^? 

melting. 

sun  by  a  column  of  ice  2.1  miles  square  and  93  000000  long, 
and  if  in  some  way  the  entire  solar  radiation  could  be  concen- 
trated upon  it,  it  would  be  melted  in  one  second,  and  in  seven 
more  would  be  dissipated  in  vapor. 

Expressing  it  as  energy,  we  find  that  the  solar  radiation  is  Expressed 
nearly  100000  horse-power  continuously  for  each  square  meter  of  J 
the  sun's  surface. 

So  far  as  we  can  see,  only  a  minute  fraction  of  the  whole 
radiation  ever  reaches  a  resting  place.     The  earth  intercepts 
about  2200  0*00000'  anc^  the  other  planets  of  the  solar  system  Question  as 
receive  in  all  perhaps  from  ten  to  twenty  times  as  much.    Some-  *°  what 

*     -  J  becomes  of 

thing  like  10o  oooooo  seems  to  ^  utilized  within  the  limits  of  heat radi- 
the  solar  system.     As  for  the  rest,  science  cannot  yet  give  any  ated  into 

space. 

certain  account  01  it. 

All  the  conclusions  stated  in  the  two  preceding  sections  are 
based  on  the  assumption  that  the  sun  radiates  heat  in  all  directions 
alike,  whether  the  rays  do  or  do  not  meet  a  material  surface. 
No  reason  can  be  assigned  why  this  assumption  should  not  be 
true,  but  it  cannot  be  said  to  be  proved  as  yet,  either  by  experi- 
ment or  by  the  nature  of  the  case.  If  it  should  ever  be  shown 
to  be  incorrect,  certain  difficulties  in  the  theory  of  planetary 
evolution  would  be  greatly  mitigated. 

272.  The  Sun's  Temperature ;   Effective  Temperature.  —  As  The  temper- 
to  the  temperature  of  the  sun's  surface  we  have  no  exact  knowl-  ature °*  *he 

•*  sun:  widely 

edge,  except  that  it  must  be  higher  than  any  artificial  heat  different  at 
which  we  are  able  to  produce.    Indeed,  it  is  only  "  by  courtesy,"  different 

points* 

so  to  speak,  that  the  sun  can  be  said  to  have  a  temperature, 


252  MANUAL   OF    ASTRONOMY 

since  the  temperature  at  different  elevations  above  and  beneath 
the  surface  must  differ  enormously;  nor,  probably,  is  it  the 
same  in  a  sun-spot  as  in  the  faculse,  though  we  note  in  passing 
that  observations  indicate  no  systematic  difference  depending 
on  position  upon  the  sun's  surface,  i.e.,  on  solar  latitude  and 
longitude. 

When  we  speak  of  the  temperature  of  the  sun  we  mean 
what  is  called  the  "effective  temperature,"  i.e.,  the  temperature 
that  a  surface  of  standard  radiating  power  (lampblack  is  the 
standard)  would  require  in  order  to  radiate  heat  at  the  same 
rate  as  the  sun.  If  the  actual  surface  of  the  sun  has  a  radiat- 
ing power  inferior  to  that  of  the  standard,  as  is  probably  the 
case,  then  the  actual  mean  temperature  must  be  higher  than 
the  effective,  and  vice  versa. 

If  we  knew  absolutely  the  law  which  connects  the  radiation 
rate  of  a  surface  with  its  temperature,  we  could  compute  the 
effective  temperature  from  the  solar  constant. 

If  we  accept  as  correct  Stefan's  Law,  which  is  borne  out  by 
the  most  trustworthy  recent  laboratory  work,  viz.,  that  the  rate 
of  radiation  is  proportional  to  the  fourth  power  of  the  absolute 
temperature,1  the  sun's  "effective  temperature"  comes  out  about 
7000°  C.  or  12000°  F. 

The  highest  temperatures  artificially  obtained  in  the  electric 
arc  are  in  the  neighborhood  of  4000°  C. 

The  assumption  of  various  other  laws  of  radiation  has  led  to 
a  ridiculously  wide  range  of  computed  solar  temperatures,  all 
the  way  from  1500°  C.,  by  Pouillet,  to  the  millions  of  Secchi 
and  Ericsson.  And  the  result,  as  stated  above,  is  doubtful  by 
at  least  500°  C. 

The  burning  273.  The  Burning  Lens.  —  A  most  impressive  demonstration 
of  the  intensity  of  the  sun's  heat  lies  in  the  fact  that  in  the 
focus  of  a  powerful  burning  lens  all  known  substances  melt  and 

1  The  absolute  temperature  is  the  temperature  reckoned  from  the  absolute 
zero,  -  273°  C.  or  -  449.4  F. 


THE   SUN  253 

vaporize.  Now  at  the  focus  of  a  lens  the  temperature  can  never 
more  than  equal  that  of  the  source  from  which  the  heat  comes. 
Theoretically,  the  limit  is  that  temperature  which  would  be 
produced  by  the  sun's  direct  radiation  at  a  distance  such  that 
the  sun's  apparent  diameter  would  just  equal  that  of  the  lens 
viewed  from  its  focus. 

The  temperature  produced  at  F  (Fig.  108)  would,  if  there  Highest 
were  no  losses,  be  iust  the  same  as  that  of  a  body  placed  so 

J  J    ^  reached  by 

near  the  sun  that  the  sun's   angular  diameter  equals  LFL.  burning 
Now,  in  the  case  of  the  most  powerful  lenses  hitherto  made,  lens> 
about  4  feet  in  diameter,  a  body  at  the  focus  was  thus  virtu- 
ally carried  to  within  about  240000  miles  from  the  sun's  surface 
(the  distance  of  the  moon  from  the  earth),  and  here,  as  has  been 
said,  the  most  refractory 
substances  succumb 
immediately. 

A    corroboration    of    

the    evidence    of    the    

burning  lens  is  found  FlG  108 

in  the  great  extension 

of  the  solar  spectrum  into  the  ultra-violet  region  and  in  the 

penetrating  power  of  the  solar  rays.    Rays  coming  from  a  source 

of  comparatively  low  temperature  —  from  a  stove,  for  instance  — 

are  almost  wholly  absorbed  by  a  plate  of  glass,  while  those  of 

the  sun  pass  almost  without  loss. 

274,   Constancy  of  the  Sun's  Heat. — It  is  an  interesting  ques-  Constancy 
tion,  as  yet  unanswered,  whether  the  total  amount  of  the  sun's  of  the  sun's 

.  mi  keat:  n° 

radiation  does  or  does  not  perceptibly  vary.      There  may  be  sensible 

considerable  fluctuations  in  the  quantity  of  heat  hourly  received  chanse  for 

from  the  sun  without  our  being  able  to  detect  them  surely  with  thousand 

our  present  means  of  observation,  but  as  far  as  observations  go  years, 

there  is  no  evidence  that  the  total  amount  varies  very  much.  temporary 

As  to  any  steady,  progressive  increase  or  decrease  of  solar  fluctuations 

heat,  it  is  quite  certain  that  no  important  change  of  that  kind  a 


254 


MANUAL   OF   ASTRONOMY 


has  been  going  on  for  the  past  two  thousand  years,  because  the 
distribution  of  plants  and  animals  on  the  earth's  surface  is  practi- 
cally the  same  as  in  the  days  of  Pliny;  it  is,  however,  rather 
probable  than  otherwise  that  the  general  climatic  changes  which 
geology  indicates  as  having  formerly  taken  place  on  the  earth 
—the  glacial  and  carboniferous  epochs,  for  instance — may  ulti- 
mately be  traced  to  changes  in  the  sun's  condition. 

275.  Maintenance  of  Solar  Heat. — One  of  the  most  interesting 
and  important  problems  of  modern  science  relates  to  the  expla- 
nation of  the  method  by  which  the  sun's  heat  is  maintained. 
We  cannot  here  discuss  the  subject  fully,  but  must  content 
ourselves  with  saying,— 

(1)  Negatively,  that  the  phenomenon  cannot  be  accounted  for 
on  the  supposition  that  the  sun  is  a  hot,  solid,  or  liquid  body 
simply  cooling,  nor  by  combustion,  nor  (adequately)  by  the  fall  of 
meteoric  matter  on  the  sun's  surface,  though  this  cause  undoubt- 
edly operates  to  a  limited  extent. 

(2)  Positively,  the  solar  radiation  can  be  accounted  for  on  the 
hypothesis,  proposed  first  by  Helmholtz,  that  the  sun  is  shrinking 
slowly  but  continuously.     It  is  a  matter  of  demonstration  that 
an  annual  shrinkage  of  about  200  feet  in  the  sun's  diameter 
would  liberate  heat  sufficient  to  keep  up  its  present  observed 
radiation  without  any  fall  in  its  temperature.     If  the  shrinkage 
were  more  than  200  feet,  the  sun  would  be  hotter  at  the  end 
of  a  year  than  it  was  at  the  beginning. 

It  is  not  possible  to  exhibit  this  hypothetical  shrinkage  as  a  fact  of 
observation,  since  this  diminution  of  the  sun's  diameter  would  amount  to 
a  mile  only  in  26.4  years,  and  nearly  ten  thousand  years  would  be  spent 
in  reducing  it  by  a  single  second  of  arc.  No  change  much  smaller  than 
V  could  be  certainly  detected  even  by  our  most  modern  instruments. 

We  can  only  say  that  while  no  other  theory  yet  proposed  meets 
the  conditions  of  the  problem,  this  appears  to  do  so  perfectly,  and 
therefore  has  high  probability  in  its  favor,  especially  as  it  appears  to  be 
a  mere  continuation  of  the  process  by  which  the  present  solar  system  was 
evolved. 


THE   STINT  255 

276.  Lane's  Law.  —  It   was   first   pointed  out  by  Lane  of  Lane's  Law: 
Washington  in  1870  that  a  gaseous  body,  losing  heat  by  radia-  amasso 
tion  and  contracting  under  its  own  gravity,  must  rise  in  tempera-  tracting 
ture  until  it  ceases  to  be  a  "perfect  gas,"  either  by  beginning  to  under  its . 
liquefy,  or  by  reaching  a  density  at  which  the  laws  of  "perfect  from  ioss  of 
gases"  cease  to  hold.     In  a  mass  of  perfect  gas  the  "work"  heat,  rises  in 
due  to  its  shrinkage  (like  the  work  done  by  a  descending  clock  untiiit 
weight)  is  more  than  sufficient  to  replace  the  loss  of  tempera-  ceases  to  be 
ture  due  to  its  radiation,  and  it  therefore  becomes  hotter.     This  jja^er 

is  not  the  case  with  a  mass  of  solid  or  liquid,  which,  as  it  loses 
heat  and  begins  to  liquefy  or  solidify,  diminishes  in  temperature 
as  well  as  dimensions,  and  grows  colder. 

It  appears  that  in  the  sun  at  present  the  relative  proportion 
of  true  gases  and  liquids  (the  droplets  which  form  the  pho- 
tospheric  clouds)  is  such  as  to  keep  the  temperature  nearly 
stationary, — a  condition  which  may  endure  for  thousands  of 
years. 

CONSTITUTION   OF   THE   SUN 

The  now  generally  received  opinion  on  this  subject  may  be 
summed  up  substantially  as  follows : 

277.  The  Central  Nucleus.  —  As  to  the  condition  of  this  we  The  central 
cannot  claim  certain  knowledge,  but  many  considerations  lead  nucleus 

gaseous. 

to  the  conclusion  that  it  is  purely  gaseous  and  has  a  temper- 
ature immensely  higher  than  that  of  the  solar  surface  even. 
But  this  central  mass,  while  gaseous  in  that  it  follows  essen- 
tially the  characteristic  laws  of  Dalton,  Boyle,  and  Charles 
(Physics,  p.  141),  must  be  greatly  condensed  by  the  enormous 
pressure  due  to  solar  gravity ;  denser  than  water,  and  viscous,  so 
to  speak,  like  tar  or  pitch  in  resisting  rapid  motion  within  it. 

Certain  phenomena,  however,  such  as  the  tendency  of  photo- 
spheric  disturbances  (sun-spots  and  faculse)  to  break  out  repeat- 
edly in  the  same  region  (Sec.  237),  suggest  something  like  a 
quasi-solidity,  sufficient  to  lead  to  the  definite  localization  of 


256 


MANUAL   OF   ASTRONOMY 


The  photo- 
cTomTsheet 


Difficulties 
of  the  cloud- 
sheet  theory. 


Schmidt's 
optical 
theory  of 
the  photo- 
sphere. 


certain  conditions  at  certain  points  below  the  photosphere ;  and 
there  are  other  phenomena  which  rather  tend  in  the  same  direc- 
tion. Indeed,  there  are  some  who  still  hold  to  a  solid  or  liquid 
nucleus  for  the  sun. 

278.  The  Photosphere.  —  The  photosphere  is  believed  to  be  a 
sheet  of  luminous  clouds,  constituted  mechanically  like  terres- 
trial clouds,  i.e.,  of  minute  solid  or  liquid  particles  floating 
in  gas.  These  photospheric  clouds  are  supposed  to  be  formed 
(just  as  clouds  of  rain  and  snow  are  formed  in  our  own  atmos- 
phere) by  the  cooling  and  condensation  of  vapors  at  the  solar 
surface  where  they  are  exposed  to  the  cold  of  outer  space,  and 
they  float  in  the  permanent  gases  of  the  solar  atmosphere  in  the 
same  way  that  our  own  clouds  do  on  our  own  atmosphere. 

We  do  not  know  precisely  what  materials  constitute  the 
photosphere,  but  naturally  suppose  them  to  be  those  indicated 
by  the  Fraunhofer  lines,  i.e.,  chiefly  the  metals,  with  carbon  and 
its  chemical  congeners. 

But  this  cloud  theory  of  the  photosphere  is  not  without  its  difficulties. 
It  is  embarrassed  by  the  fact  that  we  know  of  no  substance  that  remains 
solid  or  liquid,  even  at  a  temperature  anywhere  near  that  which  seems  to 
prevail  at  the  solar  surface.  Carbon,  perhaps  the  most  refractory  of  known 
substances,  vaporizes  completely  at  a  temperature  of  about  7000°  F.  Still 
the  temperature  of  12000°  F.  ascribed  to  the  solar  surface  is  only  the 
"effective"  average  temperature,  and  possibly  is  not  inconsistent  with  the 
hypothesis  that  the  "granules"  of  the  photosphere  are  due  to  local  cool- 
ings caused  by  explosive  expansion  of  vapors  forced  up  from  below  by 
tremendous  pressure  into  or  through  a  gaseous  envelope  of  much  higher 
temperature. 

Some  are  disposed  to  evade  the  difficulty  by  invoking  an  electrical 
action  of  some  kind,  but  as  yet  in  too  vague  a  manner  to  permit  intelligent 
criticism. 

We  merely  mention  an  ingenious  theory  proposed  a  few  years  ago 
by  Prof.  A.  Schmidt  of  Stuttgart,  viz.,  that  the  photosphere  is  a  purely 
optical  phenomenon,  a  sort  of  mirage  so  to  speak,  the  sun  itself  being 
entirely  gaseous.  The  theory,  based  wholly  on  optical  principles,  has 
some  strong  points;  but  it  ignores  many  spectroscopic  facts,  and  the 


THE   SUN  257 

fundamental  laws  of  physics  seem  to  make  it  certain  that  a  globe  contain- 
ing iron  and  the  other  metals  in  the  state  of  vapor  must  inevitably  form  a 
photospheric  shell  of  "  cloud "  in  the  outer  portions  exposed  to  radiation, 
thus  "clothing  itself  with  light  as  with  a  garment." 

279,  The  Solar  Atmosphere;    the  Reversing  Layer,  Chromo-  Therevers- 
sphere,  and  Prominences.  —  As  has  just  been  said,  the  photo-  inslayer: 

,       .        ,        ,      n  11  the  part  of 

spheric  clouds  lioat  in,  and  under,  an  atmosphere  containing  the  solar 
a  considerable  quantity  of  the  same  vapors  out  of  which  they  atmosphere 
themselves  have  been  formed.     This  vapor-laden  atmosphere,  enveloping 
probably  comparatively  shallow,  constitutes  the  reversing  layer,  the  photo- 
By  its  general  absorption  it  produces  the  peculiar  darkening  at 
the  limb  of  the  sun,  and  by  its  selective  absorption  it  produces 
the  dark  Fraunhofer  lines  or  solar  spectrum.    It  will  be  remem- 
bered that  Sir  Norman  Lockyer  and  others  have  been  disposed 
to  question  the  existence  of  any  such  shallow  absorbing  stratum, 
but  that  the  photographs  made  at  the  recent  eclipses  seem  to 
establish  its  reality. 

The  chromosphere  and  prominences  are  chiefly  composed  of  Thechromo- 
permanent  gases,  mainly  hydrogen,  helium,  and  calcium,  which,  sPhere  and 
near  the  photosphere,  are  mingled  with  the  vapors  of  the  revers-  nences 
ing  stratum,  but  rise  to  far  greater  elevations  than  those  vapors,  composed 
The  appearances  are  for  the  most  part  as  if  the  chromosphere  p^rma^ent 
were  formed  of  jets  of  heated  gases,  ascending  through  the  inter-  gases, 
spaces  between  the  photospheric  clouds,  like  flames  playing  over 
a  coal  fire. 

280.  The  Corona  also  rests  at  its  base  on  the  photosphere,  The  corona 
and  the  characteristic  green  line  of  its  spectrum  is  brightest  just  stm  to  a 

,,•,-»  ^,  i  •      ,1  .  -,    great  extent 

at  the  surtace  01  the  photosphere,  in  the  reversing  stratum,  and  a  mystery. 

in  the  chromosphere  itself ;  but  it  extends  far  beyond  even  the 

loftiest  prominences  to  distances  sometimes  of  several  millions 

of  miles.     It  seems  to  be  not  entirely  gaseous,  but  to  contain, 

in  addition  to  the  mysterious  coronium,  dust  and  fog  of  some 

sort,  very  likely  of  meteoric  origin.     Many  of  the  phenomena 

of  the  corona  are  still  unexplained,  and  since  thus  far  it  has 


258 


MANUAL   OF   ASTRONOMY 


been  observable  only  during  the  brief  moinenis  of  solar  eclipses, 
progress  in  its  study  has  been  necessarily  slow.  No  observer 
has  yet  seen  the  corona  for  a  sum  total  of  time  amounting  to 
fifteen  minutes. 

Fig.   109   (from   The   Sun,   by  permission  of   D.  Apple  ton 
&  Co.)  presents  the  theory  stated  above,  though  the  distinction 


FIG.  109.  —  Constitution  of  the  Sun 
From  The  Sun,  by  permission  of  the  publishers 

between  the  photospheric  cloud  shell  and  the  chromosphere  is 
hardly  brought  out  as  clearly  as  desirable ;  nor  is  it  certain  that 
all  the  spots  are  cavities,  as  represented. 


HE   SUN  259 


EXERCISES 

1.  Assuming  Faye's  equation  (Sec.  230)  for  the  solar  rotation,  what  are 
the  rotation  periods  at  the  sun's  equator,  in  solar  latitude  30°,  in  latitude 
45°,  and  at  the  pole  ?  f  At  equator,  25.06  days. 

,  Lat.  30°,  26.49  « 
Lat.  45°,  28.09  « 
At  pole,  31.95  " 

2.  Assuming  Spoerer's  equation  (Sec.  230),  what  would  be  the  results? 

3.  What  would  be  the  synodic  or  apparent  time  of  rotation  for  a  spot  in 
latitude  45°  according  to  Faye's  equation?  Ans.    30.43  days. 

Z/4.  If  the  diameter  of  the  sun   were  doubled,   its  density  remaining 
unchanged,  what  would  be  the  force  of  gravity  at  its  surface? 

5.  If  the  sun  were  expanded  into  a  homogeneous  sphere,  with  a  radius 
equal  to  the  distance    of   the   earth   from   the  sun,   its  mass  remaining 
unchanged,  what  would  be  the  force  of  gravity  at  its  surface? 

Ans-    i<m»  of  g. 

6.  In  this  case,  what  change,  if  any,  would  result  in  the  orbit  of  the 
earth?  Ans.   None. 

7.  In  the  neighborhood  of  a  sun-spot  a  point  is  found  in  its  spectrum 
where  a  portion  of  the  C  line  (A  =  6563.0)  is  deflected  to  6566.0.     What 
is  the  velocity  (in  the  line  of  sight)  of  the  hydrogen  at  that  point  ?     (See 
Sec.  255.)  Ans.    85.17  miles  receding. 

8.  How  great  is  the  displacement  of  the  hydrogen  line  F  (X  =  4861.5) 
at  that  point?  Ans.    2.22  units  (of  wave-length). 

9.  How  great  a  displacement  is  produced  in  the  line  D  (A.  =  5896.16) 
by  a  velocity  of  100  miles  a  second?  Ans.    3.16  units. 

10.  If  a  luminous  body  were  moving  towards  us  with  a  velocity  one 
fourth  that  of  light,  what  would  be  the  effect  upon  the  apparent  length  of 
the  portion  of  the  spectrum  included  between  two  given  lines,  —  say  C 
and  F? 

11.  What  if  it  were  moving  towards  us  with  the  speed  of  light,  and 
what  if  it  were  receding  at  that  rate  ? 

12.  What  if  the  observer  were  receding  with  the  speed  of  light,  and 
what  if  he  were  moving  towards  it  at  that  rate? 


260  MANUAL   OF   ASTRONOMY 

13.  If  the  diameter  of  the  sun  is  decreasing  at  the  rate  of  300  feet  a 
year,  how  long  before  its  apparent  diameter  will  have  decreased  by  1"? 

Ans.   7927  years. 

14.  If  the  rate  of  shrinkage  be  assumed  to  continue  uniform  (i.e.,  300 
feet  a  year  —  an  impossible  assumption),  how  long  would  it  be  before  its 
diameter  is  diminished  by  1%?  Ans.   Over  150000  years. 

/  15.  How  much  would  its  mean  density  then  be  increased  ? 

Ans.   About  3%. 

16.  Taking  the  "  calory  "  as  equivalent  to  428  kilogrammeters  of  energy, 
what  weight  falling  100  meters  to  the  surface  of  the  earth  would,  at  the 
end  of  its  fall,  possess  an  energy  equal  to  that  of  the  solar  radiation 
received  in  an  hour  upon  10  square  meters  of  the  earth's  surface,  admitting 
a  loss  of  50%  absorbed  by  the  air  ?  Ans.   38520  kgm. 

17.  Assuming  that  sunlight  at  the  earth  equals  70000  times  that  of  a 
standard  candle  at  a  distance  of  1  meter,  at  what  distance  would  the  light 
of   the  sun  equal  that   of   a  2000    candle-power   electric  arc   10  meters 
distant?  -4ns.    About  59  times  the  earth's  distance. 

18.  How  does  the  illumination  of  a  surface  by  an  arc-light  of  2000 
candle-power  at  a  distance  of  1  meter  compare  with  its  illumination  by 
sunlight?  Ans.  -fa. 

NOTE  TO  SEC.  242 

Recent  photographs  of  hydrogen  flocculi  obtained  at  Mt.  Wilson  with 
Hale's  spectroheliograph  have  shown  unmistakable  evidence  of  the  exist- 
ence of  cyclonic  storms  or  vortices  in  connection  with  several  different 
spots.  Investigations  now  in  progress  may  lead  to  a  substantial  revision  of 
sun-spot  theories. 

For  a  full  account  of  the  work  of  Professor  Hale  and  his  associates  the 
student  is  referred  to  the  Contributions  from  the  Solar  Observatory,  published 
by  the  Carnegie  Institution. 


CHAPTER   X 
ECLIPSES 

Form  and  Dimensions  of  Shadows  —  Eclipses  of  the  Moon  —  Solar  Eclipses  — 
Total,  Annular,  and  Partial  —  Ecliptic  Limits  and  Number  of  Eclipses  in  a  Year 
—  Recurrence  of  Eclipses  and  the  Saros  —  Occultations 

281.  The  word  "eclipse"  is  a  term  applied  to  the  darkening 
of  a  heavenly  body,  especially  of  the  sun  or  moon,  though  some 
of  the  satellites  of  other  planets  besides  the  earth  are  also 
"eclipsed."     An  eclipse  of  the  moon  is  caused  by  its  passage  Eclipses 
through  the  shadow  of  the  earth;  eclipses  of  the  sun,  by  the  causedby 

shadows. 

interposition  of  the  moon  between  the  sun  and  the  observer,  or, 
what  comes  to  the  same  thing,  by  the  passage  of  the  moon's 
shadow  over  the  observer. 

The  shadow  which  causes  an  eclipse  is  the  space  from  which  Shadows  of 
sunlight  is   excluded  by  an  intervening  body;  geometrically  earthand 
speaking,  it  is  a  solid,  not  a  surface.     If  we  regard  the  sun  and  cones, 
the  other  heavenly  bodies  as  spherical,  these  shadows  are  cones 
with  their  axes  in  the  line  joining  the  centers  of  the  sun  and 
the  shadow-casting  body,  the  point  being  always  directed  away 
from  the  sun. 

282.  Dimensions  of  the  Earth's  Shadow.  — The  length  of  the  Dimensions 
earth's  shadow  is  easily  found.     In  Fig.  110  we  have,  from  ofthe 

J  shadow  of 

the  similar  triangles,   OED  and  ECa,  the  earth. 

OD'.OEnEa:  EC,  or  L. 

OD  is  the  difference  between  the  radii  of  the  sun  and  the  earth, 
=  R  —  r.  Ea  =  r,  and  OE  is  the  distance  of  the  earth  from  the 
sun  =  D.  Hence,  /  '  r  \ 

L  =  D  \R-rJ  = 

261 


262 


MANUAL   OF   ASTRONOMY 


(The  fraction  108.5  is  found  by  simply  substituting  for  R  and 

Length  of      r  their  values,  R  being  109.5  X  r.)     This  gives  857000  miles 

for  the  length  of  the  earth's  shadow  when  D  has  its  mean  value 

shadow 

857000 miles,  of  93  000000  miles.  The  length  varies  about  14000  miles  on 
each  side  of  the  mean,  in  consequence  of  the  variation  of  the 
earth's  distance  from  the  sun  at  different  times  of  the  year. 

From  the  cone  a  Cb  all  sunlight  is  excluded,  or  would  be  were 
it  not  for  the  fact  that  the  atmosphere  of  the  earth  by  its  refrac- 
tion bends  some  of  the  rays  into  this  shadow.  The  effect  of 


The 
penumbra. 


Boundaries 
of  shadow 
and  pe- 
numbra opti- 
cally indefi- 
nite, though 
geometrically 
definite. 


Flo.  110.  —  The  Earth's  Shadow 

this  atmospheric  refraction  is  to  increase  the  diameter  of  the 
shadow  about  two  per  cent  where  the  moon  crosses  it,  but  to 
make  it  less  perfectly  dark. 

283.  Penumbra.  —  If  we  draw  the  lines  Ba  and  Ab  (Fig.  110), 
crossing  at  P,  between  the  earth  and  the  sun,  they  will  bound 
the  penumbra,  within  which  a  part,  but  not  the  whole,  of  the 
sunlight  is  cut  off ;  an  observer  outside  of  the  shadow  but 
within  this  cone  frustum,  which  tapers  towards  the  sun,  would 
see  the  earth  as  a  black  body  encroaching  on  the  sun's  disk. 

While  the  boundaries  of  the  shadow  and  penumbra  are  per- 
fectly definite  geometrically,  they  are  not  so  optically.  If  a 
screen  were  placed  at  Jf,  perpendicular  to  the  axis  of  the  shadow, 
no  sharply  defined  lines  would  mark  the  boundaries  of  either 
shadow  or  penumbra.  Near  the  edge  of  the  shadow  the  penum- 
bra would  be  very  nearly  as  dark  as  the  shadow  itself,  only  a 


ECLIPSES  263 

mere  speck  of  the  sun  being  there  visible;  and  at  the  outer 
edge  of  the  penumbra  the  shading  would  be  still  more  gradual. 

284,  Eclipses  of  the  Moon.  —  The  axis,  or  central  line,  of  the 
earth's  shadow  is  always  directed  to  a  point  directly  opposite 
the  sun.      If,  then,  at  the  time  of  the  full  moon,  the  moon 
happens  to  be  near  the  ecliptic  (i.e.,  not  far  from  one  of  the  Why 
nodes  of  her  orbit),  she  will  pass  through  the  shadow  and  be  e^hPses 

of  moon  do 

eclipsed.     Since,  however,  the  moon's  orbit  is  inclined  to  the  not  occur 
ecliptic   at  an  average  angle  .of  5°  8',  lunar  eclipses  do  not  at  every 

full  moon. 

happen  very  frequently,  —  seldom  more  than  twice  a  year. 
Ordinarily  the  full  moon  passes  north  or  south  of  the  shadow 
without  touching  it. 

Lunar  eclipses  are  of  two  kinds,  —  partial  and  total :  total  Partial  and 
when  she  passes  completely  into  the  shadow,  partial  when  she  ^henioon 
only  partly  enters  it,  going  so  far  to  the  north  or  south  of  the 
center  of  the  shadow  that  only  a  portion  of  her  disk  is  obscured. 

285.  Size  of  the  Earth's  Shadow  at  the  Point  where  the  Moon  Diameter 
crosses  it.  —  Since  EC,  in  Fig.  110,  is  857000  miles,  and  the  ofearth's 

'  shadow 

distance  01  the  moon  irom  the  earth  is  on  the  average  about  where  the 
239000  miles,   CM  must  average  618000  miles,  so  that  MN,  moon 
the  semidiameter  of  the  shadow  at  this  point,  will  be  |^|  of  the 
earth's  radius.      This  gives  MN=  2854  miles,  and  makes  the 
whole  diameter  of  the  shadow  a  little  over  5700  miles,  — about 
two  and   two-thirds  times   the   diameter  of   the  moon.      But 
this  quantity  varies  considerably  with  the  moon's  distance ;  the 
shadow,  where  she  crosses  it,  is  sometimes  more   than  three 
times  her  diameter,  sometimes  hardly  more  than  twice. 

An  eclipse  of  the  moon,  when  central,  i.e.,  when  the  moon 
crosses  the  center  of  the  shadow,  may  continue  total  for  about 
two  hours,  the  interval  from  the  first  contact  to  the  last  being  Duration  of 
about  two  hours  more.     This  depends  upon  the  fact  that  the  aliunar 
moon's  hourly  motion  is  nearly  equal  to  its  own  diameter. 

The    duration    of   a   non-central   eclipse   varies,    of   course, 
according  to  the  part  of  the  shadow  traversed  by  the  moon. 


264 


MANUAL   OF   ASTRONOMY 


Lunar 
ecliptic 
limits : 
9°3<Xto 
12°  15'. 


Phenomena 
of  a  lunar 
eclipse. 


286.  Lunar  Ecliptic  Limit.  —  The  lunar  ecliptic  limit  is  the 
greatest  distance  from  the  node  of  the  moon's  orbit  at  which 
the  sun  can  be  at  the  time  of  a  lunar  eclipse.     This  limit 
depends  upon  the  inclination  of  the  moon's  orbit,   which  is 
somewhat  variable,  and  also  upon. the  distance  of  the  moon 
from  the  earth  at  the  time  of  the  eclipse,  which  is  still  more  vari- 
able.    Hence,  we  recognize  two  limits,  —  the  major  and  minor. 

If  the  distance  of  the  sun  from  the  node  at  the  time  of  full 
moon  exceeds  the  major  limit,  an  eclipse  is  impossible ;  if  it  is 
less  than  the  minor,  an  eclipse  is  inevitable.  The  major  limit 
is  found  to  be  12°  15';  the  minor,  9°  30'. 

Since  the  sun,  in  its  annual  motion  along  the  ecliptic,  travels 
12°  15'  in  less  than  thirteen  days,  it  follows  that  every  eclipse 
of  the  moon  must  take  place  within  thirteen  days  from  the  time 
when  the  sun  crosses  the  node. 

287.  Phenomena  of  a  Total  Lunar  Eclipse.  —  Half  an  hour  or 
so  before  the  moon  reaches  the  shadow,  its  limb  begins  to  be 


M 


FIG.  111.  — Light  bent  into  Earth's  Shadow  by  Kefraction 

sensibly  darkened  by  the  penumbra,  and  the  edge  of  the  shadow 

itself  when  it  first  attacks  the  moon  appears  nearly  black  by 

contrast  with  the  bright  parts  of  the  moon's  surface.     To  the 

naked  eye  the  outline  of  the  shadow  looks  reasonably  sharp; 

but  even  with  a  small  telescope  it  is  found  to  be  indefinite,  and 

with  a  large  telescope  and  high  magnifying  power  it  becomes 

entirely  indistinguishable,  so  that  it  is  impossible  to  determine 

Moment  of     within  about  half  a  minute   the  time  when  the  boundary  of 

beginning  not  ^  s}ia(jow  reaches  any  particular  point  on  the  moon.     After 

observable,    the  moon  has  wholly  entered  the  shadow  her  disk  is  usually 


ECLIPSES  265 

distinctly  visible,  illuminated  with  a  dull,  copper-colored  light, 
which  is  sunlight,  deflected  around  the  earth  into  the  shadow 
by  the  refraction  of  our  atmosphere,  as  illustrated  by  Fig.  111. 

Even  when  the  moon  is  exactly  central  in  the  largest  possible  shadow, 
an  observer  on  the  moon  would  see  the  disk  of  the  earth  surrounded  by  a 
narrow  ring  of  brilliant  light,  colored  with  sunset  hues  by  the  same  vapors   Color  of 
which  tinge  terrestrial  sunsets,  but  acting  with  double  power  because  the   ^e  eclipsed 
light  has  traversed  a  double  thickness  of  our  air.     If  the  weather  happens   moon; 
to  be  clear  at  this  portion  of  the  earth  (upon  its  rim,  as  seen  from  the    ca      d  h 
moon),  the  quantity  of  light  transmitted  through  our  atmosphere  is  very   light  de- 
considerable,  and  the  moon  is  strongly  illuminated.     If,  on  the  other  hand,    fleeted  into 
the  weather  happens  to  be  stormy  in  this  region  of  the  earth,  the  clouds  cut  the  shadow 
off  nearly  all  the  light.     In  the  lunar  eclipse  of  1884  the  moon  was  abso-     JT  °ur  . 
lutely  invisible  for  a  time  to  the  naked  eye,  —  a  very  unusual  circumstance 
on  such  an  occasion. 

The  heat  radiation  of  the  moon,  according  to  the  observa- 
tions of  Lord  Rosse,  falls  off  during  the  progress  of  the  eclipse, 
almost  in  the  same  ratio  with  the  light.     At  the  moment  when 
the  eclipse  becomes  total  fully  ninety-eight  per  cent  of  the  heat  Effect  upon 
has  disappeared,  and  half  of. the  remaining  two  per  cent  is  lost  *•  e  mo°n's 
during  the  totality.     As  the  light  returns  the  heat  rises  almost  ation. 
as  rapidly  as  it  fell,  showing  that  the  moon's  surface  has  very 
little   power  of  storing  heat,  —  a  natural   consequence   of  its 
airlessness ;   but  it  is  several  hours  before  the  heat  radiation 
recovers  fully  the  value  it  had  before  the  eclipse. 

If  the  eclipse  is  well  visible  in  both  hemispheres,  arrange- 
ments are  usually  made  to  observe  as  many  star  occultations  as 
possible  during  the  totality,  for  the  purpose  of  determining  the 
moon's  place  and  parallax,  and  for  other  purposes  also. 

288.   Computation  of  a  Lunar  Eclipse.  —  Since  all  the  phases  Why  the 
of  a  lunar  eclipse  are  seen  everywhere  at  the  same  absolute  calculation 

J  g  of  a  lunar 

instant  wherever  the  moon  is   above  the  horizon,   it  follows  eclipse  is 
that  a  single  computation  giving  the  Greenwich  times  of  the  simPle- 
different  phenomena  is  all  that  is  needed.     Such  computations 
are   made    and   published   in   the   Nautical   Almanac.      Each 


266  MANUAL   OF   ASTRONOMY 

observer  has  only  to  correct  the  predicted  time  by  simply 
adding  or  subtracting  his  longitude  from  Greenwich,  in  order 
to  get  the  true  local  time.  The  computation  of  a  lunar  eclipse 
is  not  at  all  complicated. 

For  the  method  of  projecting  and  computing  a  lunar  eclipse,  see  Appen- 
dix, Sees.  703  and  704. 

ECLIPSES   OF   THE   SUN 

289.    Dimensions    of    the   Moon's    Shadow.  —  By   the    same 

Length  of       method  as  that  used  for  the  shadow  of  the  earth  (Sec.  282)  we 

tie  moon's     £n(j  ^at  ^Q  length  of  the  moon's  shadow  at  any  time  is  very 

B 


m >  To  Sun 

FIG.  112.  —  The  Moon's  Shadow  on  the  Earth 

nearly  ^^  of  its  distance  from  the  sun,  and  averages  232150 
miles.  It  varies  not  quite  4000  miles  each  way,  ranging  from 
228300  to  236050  miles. 

Since  the  mean  length  of  the  shadow  is  less  than  the  mean 
distance  of  the  moon  from  the  earth  (238800  miles),  it  is  evi- 
dent that  on  the  average  the  shadow  will  not  reach  the  earth. 

On  account  of  the  eccentricity  of  the  moon's  orbit,  she  is 
much  of  the  time  considerably  nearer  than  at  others  and  may 
Maximum  come  within  221600  miles  from  the  earth's  center,  or  about 
217650  miles  from  its  surface.  If  at  the  same  time  the  shadow 
happens  to  have  its  greatest  possible  length,  °';s  point  may  reach 
nearly  18400  miles  beyond  the  earth's  surface.  In  this  case 
the  cross-section  of  the  shadow  where  the  earth's  surface  cuts 
it  squarely  (at  o  in  Fig.  112)  will  be  about  168  miles  in  diam- 
eter, which  is  the  largest  value  possible.  If,  however,  the  shadow 
strikes  the  earth's  surface  obliquely,  the  shadow  spot  will  be 


ECLIPSES  267 

oval  instead  of  circular,  and  the  extreme  length  of  the  oval  may 
much  exceed  the  168  miles. 

Since  the  distance  of  the  moon  may  be  as  great  as  252970  miles 
from  the  earth's  center,  or  nearly  249000  miles  from  its  surface, 
while  the  shadow  may  be  as  short  as  228300  miles,  we  may  have 
the  state  of  things  indicated  by  placing  the  earth  at  B  in  Fig.  112.  Maximum 
The  vertex  of  the  shadow,  V,  will  then  fall  20700  miles  short  of  ^a™ter 
the  surface,  and  the  cross-section  of  the  shadow  produced  will  shadow 
have  a  diameter  of  196  miles  at  0',  where  the  earth's  surface  Produced 
cuts  it.     When  the  shadow  falls  near  the  edge  of  the  earth  the 
breadth  of  this  cross-section  may  be  as  great  as  230  miles. 

290,  Total  and  Annular  Eclipses.  —  To  an  observer  within  Total  and 
the  true  shadow  cone  (i.e.,  between  Fand  the  moon  in  Fig.  112) 

the  sun  will  be  totally  eclipsed.  An  observer  in  the  "pro- 
duced "  cone  beyond  V  will  see  the  moon  smaller  than  the  sun, 
leaving  an  uneclipsed  ring  around  it,  and  will  have  what  is 
called  an  annular,  or  "ring-formed,"  eclipse.  These  annular 
eclipses  are  considerably  more  frequent  than  the  total,  and  now 
and  then  an  eclipse  is  annular  in  part  of  its  course  across  the 
earth  and  total  in  part.  (The  point  of  the  moon's  shadow 
extends  in  this  case  beyond  the  nearest  part  of  the  surface  of 
the  earth,  but  does  not  reach  as  far  as  its  center.) 

291.  The  Penumbra  and  Partial  Eclipses.  —  The  penumbra  can 
easily  be  shown  to  have  a  diameter  on  the  line  CD  (Fig.  112)  Width  of 
of  a  trifle  more  than  twice  the  moon's  diameter.     An  observer  the  ^ejts  of 

partial 

situated  within  the  penumbra  has  a  partial  eclipse.     If  he  is  eclipse  on 

near  the  cone  of  the  shadow,  the  sun  will  be  mostly  covered  eacnsideof 

the  central 
by  the  moon;  but  if  near  the  outer  edge  of  the  penumbra,  the  ime. 

moon  will  only  slightly  encroach  on  the  sun's  disk.  While, 
therefore,  total  and  annular  eclipses  are  visible  as  such  only  by 
an  observer  within  the  narrow  path  traversed  by  the  shadow 
spot,  the  same  eclipse  will  be  visible  as  a  partial  one  every- 
where within  2000  miles  on  each  side  of  the  path.  The  2000 
miles  is  to  be  reckoned  perpendicularly  to  the  axis  of  the 


268 


MANUAL   OF   ASTRONOMY 


Velocity  of 
the  moon's 
shadow  over 
the  earth's 
surface. 


shadow,  and  may  correspond  to  a  much  greater  distance  on  the 
spherical  surface  of  the  earth. 

292.  Velocity  of  the  Shadow  and  Duration  of  Eclipses.  —  Were 
it  not  for  the  earth's  rotation,  the  moon's  shadow  would  pass  an 
observer  at  the  rate  of  nearly  2100  miles  an  hour  on  the  average. 
The  earth,  however,  is  rotating  towards  the  east  in  the  same 
general  direction  as  that  in  which  the  shadow  moves,  and  at 
the  equator  its  surface  moves  at  the  rate  of  about  1040  miles 
an  hour.  An  observer,  therefore,  on  the  earth's  equator  with 
the  moon  at  its  mean  distance  from  the  earth  and  near  the 
zenith  would,  on  the  average,  be  passed  by  the  shadow  with  a 
speed  of  about  1060  miles  an  hour  (2100-1040),  —  about 
equal  to  that  of  a  cannon-ball.  In  higher  latitudes,  where  the 
surface  velocity  due  to  the  earth's  rotation  is  less,  the  relative 
speed  of  the  shadow  is  higher ;  and  where  the  shadow  falls  very 
obliquely,  as  it  does  when  an  eclipse  occurs  near  sunrise  or 
sunset,  the  advance  of  the  shadow  on  the  earth's  surface  may 
become  very  swift,  —  as  great  as  4000  or  5000  miles  an  hour. 

A  total  eclipse  of  the  sun  observed  at  a  station  near  the 
equator,  under  the  most  favorable  conditions  possible,  may  con- 
tinue total  for  7m588.  In  latitude  40°  the  duration  can  barely 
equal  6im.  The  greatest  possible  excess  of  the  apparent 
semidiameter  of  the  moon  over  that  of  the  sun  is  only  V  19". 

At  the  equator  an  annular  eclipse  may  last  for  12m248,  the 
maximum  width  of  the  ring  of  the  sun  visible  around  the  moon 
being  1'  37". 

In  the  observation  of  an  eclipse  four  contacts  are  recognized :  the  first 
when  the  edge  of  the  moon  first  touches  the  edge  of  the  sun,  the  second 
when  the  eclipse  becomes  total  or  annular,  the  third  at  the  cessation  of  the 
total  or  annular  phase,  and  the  fourth  when  the  moon  finally  leaves  the 
solar  disk.  From  the  first  contact  to  the  fourth  the  time  may  be  a  little 
over  four  hours. 


Solar  ecliptic      293.   The  Solar  Ecliptic  Limits.  —  It  is  necessary,  in  order  to 
limits.  have  an  eclipse  of  the  sun,  that  the  moon  should  encroach  on 


Maximum 
possible 
duration  of 
a  total  solar 
eclipse  7m58'. 


Maximum 
for  an 
annular 
eclipse 
12m24'. 


ECLIPSES 


269 


the  cone  ACBD  (Fig.  113),  which  envelops  the  earth  and  sun. 
In  this  case  the  true  angular  distance  between  the  centers  of 
the  sun  and  moon,  i.e.,  their  distance  as  seen  from  the  center  of 
the  earth,  would  be  the  angle  MES.1  This  angle  may  range 
from  1°  34'  13"  to  1°  24'  19",  according  to  the  changing  dis- 
tance of  the  sun  and  moon  from  the  earth.  The  corresponding 
distances  of  the  sun  from  the  node,  taking  into  account  also 
the  variations  in  the  inclination  of  the  moon's  orbit,  give 
18°  31'  and  15°  21'  for  the  major  and  minor  ecliptic  limits. 

In  order  that  an  eclipse  may  be  central  (total  or  annular)  at 
any  part  of  the  earth,  it  is  necessary  that  the  moon  should  lie 


Limits  for 
partial 
eclipse 
15°  21'  to 
18°  31'. 


Limits  for 
central 
eclipse  9°  55' 
to  11°  507. 


FIG.  113.  — Solar  Ecliptic  Limits 

wholly  inside  the  cone  ACBD,  as  M',  and  the  corresponding 
major  and  minor  central  ecliptic  limits  come  out  11°  50'  and 
9°  55'. 

294.   Phenomena  of  a  Solar  Eclipse.  —  There  is  nothing  of  Phenomena 
special  interest  until  the  sun  is  nearly  covered,  though  before  of  a  total 

J  solar  eclipse 

that  time  the  shadows  cast  by  the  foliage  begin  to  be  peculiar. 

The  light  shining  through  every  small  interstice  among  the  leaves, 
instead  of  forming  as  usual  a  circle  on  the  ground,  makes  a  little  crescent, 
—  an  image  of  the  partly  covered  sun. 

1 MES  equals  the  sun's  angular  semidiameter  SEA  +  the  moon's  semidiam- 
eter  MEF  +  the  angle  AEF ;  and  AEF  equals  the  difference  between  EFC, 
the  moon's  parallax,  and  CAE,  the  parallax  of  the  sun;  hence,  as  usually 
written,  MES,  the  "radius  of  the  shadow,"  =  S  +  /S'  +  P  —  p,  P  being  the 
parallax  of  the  moon,  and  p  that  of  the  sun. 


270 


MANUAL   OF   ASTRONOMY 


Effect  on 
color  of  sun- 
light just 
before  and 
after 
totality. 


Advance  of 
the  shadow, 
and  the 
shadow 
bands. 


Appearance 
of  the  corona 
and  promi- 
nences and 
of  the  stars. 


Darkness 
usually 
not  very 
intense. 


Observations 
to  be  made. 


About  ten  minutes  before  totality  the  darkness  begins  to  be 
felt,  and  the  remaining  light,  coming,  as  it  does,  from  the  edge 
of  the  sun  alone,  is  much  altered  in  quality,  being  very  deficient 
in  the  blue  and  violet,  so  that  it  produces  an  effect  very  like 
that  of  a  calcium  light  rather  than  sunshine.  Animals  are 
perplexed,  and  birds  go  to  roost.  The  temperature  falls,  and 
sometimes  dew  appears.  In  a  few  moments,  if  the  observer  is 
so  situated  that  his  view  commands  the  distant  horizon,  the 
moon's  shadow  is  seen  coming,  much  like  a  heavy  thunder- 
storm, and  advancing  with  almost  terrifying  swiftness.  Just 
before  the  shadow  reaches  the  observer,  quivering,  ripple-like 
bands  appear  on  every  white  surface;  and  immediately  on  its 
arrival,  and  sometimes  a  little  before,  the  corona  and  promi- 
nences become  visible,  while  the  brighter  planets  and  the  stars 
of  the  first  two  or  three  magnitudes  make  their  appearance. 
The  suddenness  with  which  the  darkness  falls  is  startling.  The 
sun  is  so  brilliant  that  even  the  small  portion  which  remains 
visible  up  to  within  a  very  few  seconds  of  the  total  obscuration 
so  dazzles  the  eye  that  it  is  unprepared  for  the  sudden  transition. 
In  a  few  moments,  however,  vision  adjusts  itself,  and  it  is  then 
found  that  the  darkness  is  not  really  very  intense. 

If  the  totality  is  of  short  duration  (that  is,  if  the  diameter  of 
the  moon  exceeds  that  of  the  sun  by  less  than  a  minute  of  arc), 
the  corona  and  chromosphere,  the  lower  parts  of  which  are  very 
brilliant,  give  a  light  at  least  three  or  four  times  that  of  the 
full  moon.  Since,  moreover,  in  such  a  case  the  shadow  is  of 
small  diameter,  a  large  quantity  of  light  is  also  sent  in  from  the 
surrounding  air,  where,  30  or  40  miles  away,  the  sun  is  still 
shining.  In  such  an  eclipse  there  is  not  much  difficulty  in 
reading  an  ordinary  watch  face.  In  an  eclipse  of  long  duration, 
say  five  or  six  minutes,  it  is  much  darker,  and  lanterns  become 
necessary. 

295.  Observation  of  an  Eclipse.  —  A  total  solar  eclipse  offers 
opportunities  for  numerous  observations  of  great  importance 


ECLIPSES  271 

which  are  possible  at  no  other  time,  besides  certain  others  which 
can  also  be  made  during  a  partial  eclipse.     We  mention  : 

(a)  Times  of  the  four  contacts,  and  direction  of  the  line  join- 
ing the  "  cusps  "  of  the  partially  eclipsed  sun.  These  observa- 
tions determine  with  extreme  accuracy  the  relative  positions  of 
the  sun  and  moon  at  the  moment,  (b)  The  search  for  intra- 
mercurial  planets,  (c)  Observations  of  certain  peculiar  dark 
fringes,  the  so-called  "  shadow  bands,"  which  appear  upon  the 
surface  of  the  earth  for  about  a  minute  before  and  after  totality. 
(d)  Photometric  measurement  of  the  intensity  of  light  at  dif- 
ferent stages  of  the  eclipse,  (e)  Telescopic  observations  of  the 
details  of  the  prominences  and  of  the  corona.  (/)  Spectroscopic 
observations  (both  visual  and  photographic),  upon  the  "  flash 
spectrum  "  and  upon  the  spectra  of  the  lower  atmosphere  of 
the  sun,  of  the  prominences  and  of  the  corona,  (g)  Observa- 
tions with  the  polariscope  upon  the  polarization  of  the  light 
of  the  corona,  (h)  Drawings  and  photographic  pictures  of  the 
corona  and  prominences,  (i)  Miscellaneous  observations  upon 
meteorological  changes  during  the  progress  of  the  eclipse,  — 
barometer,  thermometer,  wind,  etc.,  —  and  effects  upon  the 
magnetic  elements. 

296.   Calculation  of  a  Solar  Eclipse.  —  The  calculation  of  a  The  caicuia- 
solar  eclipse  cannot  be  dealt  with  in  any  such  summary  way  as  tlon  of  * 
that  of  a  lunar  eclipse,  because  the  times  of  contact  and  other  much  more 


phenomena  are  different  at  every  different  station.     Moreover, 
since   the  phenomena  of  a  solar  eclipse   admit  of  extremely  aiunarj 
accurate  observation,  it  is  necessary  to  take  account  of  numer-  because  the 
ous  little  details  which  are  of  no  importance  in  lunar  eclipses.  stances  <je- 
The  Nautical  Almanacs  give,  three  years  in  advance,  a  chart  of  pend  on  the 
the  track  of  every  solar  eclipse,  and  with  it  data  for  the  accurate 
calculation  of  the  phenomena  at  any  given  place. 

T.  Oppolzer,  a  Viennese  astronomer,  no  longer  living,  published  a  few 
years  ago  a  remarkable  book,  entitled  The  Canon  of  Eclipses,  containing 
the  elements  of  all  eclipses  (8000  solar  and  5200  lunar)  occurring  between 


272 


MANUAL   OF   ASTRONOMY 


Number  of 
eclipses  in 
a  year. 


The  eclipse 
months  and 
the  eclipse 
year. 


Lunar 
eclipses  in  a 
year  range 
from  none 
to  three. 


the  year  1207  B.C.  and  A.D.  2162,  with  maps  showing  the  approximate 
track  of  the  moon's  shadow  on  the  earth.  It  indicates  total  eclipses  visi^ 
ble  in  the  United  States  in  1918,  1923,  1925,  1945,  1979,  1984,  and  1994. 

297.  Number  of  Eclipses  in  a  Year — The  least  possible  num- 
ber is  two,  both  of  the  sun ;  the  largest  seven,  five  solar  and  two 
lunar  or  four  solar  and  three  lunar.  The  most  usual  number  of 
eclipses  is  four. 

The  eclipses  of  a  given  year  always  take  place  at  two  opposite 
seasons  (which  may  be  called  the  eclipse  months  of  the  year), 
near  the  times  when  the  sun  crosses  the  nodes  of  the  moon's 
orbit.  Since  the  nodes  move  westward  around  the  ecliptic 
once  in  about  nineteen  years  (Sec.  192),  the  time  occupied  by 
the  sun  in  passing  from  a  node  to  the  same  node  again  is  only 
346.62  days,  which  is  sometimes  called  the  eclipse  year. 

In  an  eclipse  year  there  can  be  but  two  lunar  eclipses,  since 
twice  the  maximum  lunar  ecliptic  limit  (2  x  12°  15')  is  less 
than  29°  6',  the  distance  the  sun  moves  along  the  ecliptic  in 
a  synodic  month;  the  sun  therefore  cannot  possibly  be  near 
enough  the  node  at  both  of  two  successive  full  moons ;  on  the 
other  hand,  it  is  possible  for  a  year  to  pass  without  any  lunar 
eclipse,  the  sun  being  too  far  from  the  node  at  all  four  of  the 
full  moons  which  occur  nearest  to  the  time  of  its  node  passage. 

In  a  calendar  year  (of  365i  days)  it  is,  however,  possible  to 
have  three  lunar  eclipses.  If  one  of  the  moon's  nodes  is  passed 
by  the  sun  in  January,  it  will  be  reached  again  in  December, 
the  other  node  having  been  passed  in  the  latter  part  of  June, 
and  there  may  be  a  lunar  eclipse  at  or  near,  each  of  these  three 
node  passages.  This  actually  occurred  in  1852  and  1898,  and 
will  happen  again  in  1917. 

As  to  solar  eclipses,  it  is  sufficient  to  say  that  the  solar  ecliptic 
limits  are  so  much  larger  than  the  lunar  that  there  must  be  at 
least  one  solar  eclipse  at  each  node  passage  of  the  year,  at  the 
new  moon  next  before  or  next  after  it ;  and  there  may  be  two, 
one  before  and  one  after,  thus  making  four  in  the  eclipse  year. 


ECLIPSES  273 

(When  there  are  two  solar  eclipses  at  the  same  node,  there  will  Solar 
always  be  a  lunar  eclipse  at  the  full  moon  between  them.)     In  ecllPses 

*  r  range  from 

the  calendar  year  a  fifth  solar  eclipse  may  come  in  if  the  first  two  to  five, 
eclipse  month  falls  in  January.     Since  a  year  with  five  solar  Greatest 
eclipses  in  it  is  sure  to  have  two  lunar  eclipses  in  addition,  P°ssible 

•          i  i  number  of 

they    will   make   up    seven   in   the    calendar  year.     This  will  eclipses  in  a 

happen  next  in  1935;    but  in  1917  there  will  also  be  seven  year  seven; 

eclipses,  —  four  of  the  sun  and  three  of  the  moon.  ber  two> 

298,  Frequency  of  Solar  and  Lunar  Eclipses.  —  Taking  the  both  of 
whole  earth  into  account,  the  solar  eclipses  are  the  more  numer- 
ous, nearly  in  the  ratio  of  three  to  two.     It  is  not  so,  however, 

with  those  which  are  visible  at  a  given  place.     A  solar  eclipse  can 
be  seen  only  from  a  limited  portion  of  the  globe,  while  a  lunar  Keiative 
eclipse  is  visible  over  considerably  more  than  half  the  earth,  —  frequency 
either  at  the  beginning  or  the  end,  if  not  throughout  its  whole  and  lunar 
duration;  and  this  more  than  reverses  the  proportion  between  eclipses, 
lunar  and  solar  eclipses  for  any  given  station. 

Solar  eclipses  that  are  total  somewhere  or  other  on  the  earth's 
surface  are  not  very  rare,  averaging  one  for  about  every  year  Bareness  of 
and  a  half.     But  at  any  given  place  the  case  is  very  different ;  ^J?1  ^* 
since  the  track  of  a  solar  eclipse  is  a  very  narrow  path  over  the  any  given 
earth's  surface,  averaging  only  60  or  70  miles  in  width,  we  find  station, 
that  in  the  long  run  a  total  eclipse  happens  at  any  given  station 
only  once  in  about  360  years. 

During  the  nineteenth  century  seven  shadow  tracks  traversed 
the  United  States,  and  there  will  be  the  same  number  in  the 
twentieth.1 

299.  Recurrence  of  Eclipses;  the  Saros.  —  It  was  known  to 
the  Chaldeans,  even  in  prehistoric  times,  that  eclipses   occur 
at  a  regular  interval  of  18yllid  (10£  days,  if  there  happen  to  be 
five  leap-years  in  the  interval).     They  named  this  period  the 

Saros.     It  consists  of  223  synodic  months,  containing  6585.32  The  Saros. 
days,  while  19  eclipse  years  contain  6585.78.     The  difference 
1  This  does  not  take  into  account  our  insular  possessions. 


274 


MANUAL   OF   ASTRONOMY 


Number  of 
eclipses  in 
one  Saros. 


Star  occulta- 
tions. 


Suddenness 
of  the  dis- 
appearance 
and  reap- 
pearance of 
the  star. 


Anomalous 

phenomena 

sometimes 

observed  at 

oeculta- 

tions. 


is  only  about  11  hours,  in  which  time  the  sun  moves  on  the 
ecliptic  about  28'. 

If,  therefore,  a  solar  eclipse  should  occur  to-day  with  the  sun 
exactly  at  one  of  the  moon's  nodes,  at  the  end  of  223  months  the 
new  moon  will  find  the  sun  again  close  to  the  node  (28'  west  of 
it),  and  a  very  similar  eclipse  will  occur  again ;  but  the  track  of 
this  new  eclipse  will  lie  about  8  hours  of  longitude  further  west 
on  the  earth,  because  the  223  months  exceed  the  even  6585  days 
"by  _3_2_  Of  a  day.  The  usual  number  of  eclipses  in  a  Saros  is 
about  seventy-one,  varying  two  or  three  one  way  or  the  other. 

300.  Occultations  of  Stars.  —  In  theory  and  computation 
the  occultation  of  a  star  is  identical  with  a  total  solar  eclipse, 
except  that  the  shadow  of  the  moon  cast  by  the  star  is  sensibly 
a  cylinder  instead  of  a  cone,  and  has  no  penumbra.  Since  the 
moon  always  moves  eastward,  the  star  disappears  at  the  moon's 
eastern  limb,  and  reappears  on  the  western.  Under  all  ordinary 
circumstances  both  disappearance  and  reappearance  are  instan- 
taneous, indicating  not  only  that  the  moon  has  no  sensible 
atmosphere,  but  also  that  the  (angular)  diameter  of  even  a  very 
bright  star  is  less  than  0".02.  Observations  of  occultations 
determine  the  place  of  the  moon  in  the  sky  with  great  accuracy, 
and  when  made  at .  a  number  of  widely  separated  stations  they 
furnish  a  very  precise  determination  of  the  moon's  parallax  and 
also  of  the  difference  of  longitude  between  the  stations. 

Occasionally  the  star,  instead  of  disappearing  suddenly  when  struck  by 
the  moon's  limb  (faintly  visible  by  "earth-shine"),  appears  to  cling  to  the 
limb  for  a  second  or  two  before  vanishing.  In  a  few  instances  it  has  been 
reported  as  having  reappeared  and  disappeared  a  second  time,  as  if  it  had 
been  for  a  moment  visible  through  a  rift  in  the  moon's  crust.  In  some 
cases  the  anomalous  phenomena  have  been  explained  by  the  subsequent 
discovery  that  the  star  was  double,  but  many  of  them  still  remain  mysteri- 
ous ;  it  is  quite  likely  that  they  were  often  illusions  due  to  physiological 
causes  in  the  observer. 


CHAPTER  XI 
CELESTIAL  MECHANICS 

The  Laws  of  Central  Force  —  Circular  Motion  —  Kepler's  Laws,  and  Newton's 
Verification  of  the  Theory  of  Gravitation  —  The  Conic  Sections  — The  Problem 
of  Two  Bodies  — The  Parabolic  Velocity  —  Exercises  —  The  Problem  of  Three 
Bodies  and  Perturbations  —  The  Tides 

IT  is  out  of  the  question  to  attempt  here  an  extended  treat- 
ment of  the  theory  of  the  motions  of  the  heavenly  bodies,  but 
there  are  certain  fundamental  facts  and  principles  easily  under- 
stood and  so  important,  and  indeed  essential,  to  an  intelligent 
comprehension  of  the  mechanism  of  the  solar  system  that  we 
cannot  pass  them  without  notice. 

301.   Motion  of  a  Body  not  acted  upon  by  Any  Force — Accord-  Motion  of 
ing  to  the  first  law  of  motion,  a  moving  body  left  to  itself  describes  fc 
a  straight  line  with  a  uniform  speed.     When,  therefore,  we  find  by  force. 
a  body  so  moving  we  may  infer  that  it  is  acted  on  by  no  force 
whatever  or,  at  least,  that  if  any  forces  are  acting,  they  exactly 
balance  each  other,  their  resultant  being  zero,  and  absolutely 
without  effect  upon  the  motion  of  the  body. 

It  is  a  common  blunder  to  speak  of  such  a  body  as  actuated 
by  a  "projectile  force,"  —  a  survival  of  the  Aristotelian  idea  Nopro- 
that  rest  is  more  natural  to  a  body  than  motion,  and  that  j^ele 
"force"  must  operate  to  keep  a  body  moving.     This  is  not  true:  required  to 
mere  motion  implies  no  acting  force.      Change  of  motion  only,  maintain 

.,,.,,  free  motion. 

either  in  speed  or  in  direction,  implies  such  action. 

With  the  notion  referred  to  there  usually  goes  another,  —  that  a  moving 
body  must  have  been  put  in  motion  by  some  force,  as  if  all  bodies  were 
once  at  rest  —  say  at  the  moment  of  creation  —  and  acquired  their  motion 
later ;  in  respect  to  which  we  have  no  knowledge. 

275 


276 


MANUAL  OF  ASTRONOMY 


Motion  of 
body  under 
force  acting 
in  the  line 
of  motion. 


Motion 
under  force 
acting  across 
line  of 
motion. 


Condition  of 

constant 

speed. 


Only  a 
single  force 
needed  to 
explain 
curvilinear 
motion. 


Law  of 
motion 
under  a 
central 
force. 


Demonstra- 
tion that  an 
impulse 


302.  Motion  under  the  Action  of  a  Force.  —  If  the  motion  of 
a  body  is  in  a  straight  line  but  with  a  varying  speed,  we  infer  a 
force  acting  directly  in  the  line  of  motion,  either  accelerating 
or  retarding.     If  the  body  a  moves  in  a  curve  (Fig.  114),  we 
know  that  some   force  is  acting  crosswise  to  the  motion  and 
towards  the  concave  side  of  the  curve.     If  the  speed  increases, 
we  know  that  the  acting  force  pulls  not  only  crosswise,  but 
forward,  as  ab,  making  an  angle  of  less  than  90°  with  the  uline 
of  motion,"  at,  tangent  to  the  curve  at  a ;  and  vice  versa  if  the 

a  motion  is  retarded. 

If  the  speed  keeps  constant,  we 
know  that  at  a  the  force  acts  along 
ac,  always  exactly  perpendicular  to 
the  line  of  motion. 

It  is  not  unusual  to  find  curvilinear 
FIG.  114.  —  Curvature  of  an  Orbit      motion  spoken  of  as  due  necessarily  to 

two  forces;    one,  the  "projectile  force," 

imagined  to  act  along  the  line  of  motion,  while  the  second  force  draws 
sidewise.  There  may  have  been  a  projectile  force  acting  in  the  past,  but 
if  so  it  is  "ancient  history";  we  need,  at  present,  in  order  to  explain  the 
facts,  the  action  of  only  a  single  force,  operating  to  change  the  direction 
or  the  speed,  or  both,  of  the  body's  motion.  From  a  curved  path  we  can 
infer  the  necessary  existence  of  but  one  force.  This  force  may  be,  and 
often  is,  the  "resultant"  of  several;  but  then  they  act  as  one,  and  only 
one  is  needed. 

303.  Laws  governing  the  Motion  of  a  Body  moving  under  the 
Action  of  a  Force  directed  to  a  Fixed  Center ;  Law  of  Areas.  — 
In  this  case  it  is  obvious  that  the  path  of  the  body  will  be  a 
curve,  concave  towards  the  center  of  force,  and  all  lying  in  one 
plane  with  that  center. 

It  is  easy  to  prove,  further,  that  it  will  move  in  such  a  way 
that  its  radius  vector  will  describe  equal  areas  in  equal  times 
around  that  point. 

Imagine  a  body  moving  uniformly  along  the  straight  line 
AB  (Fig.  115),  so  that  AB,  BC,  CL  (the  spaces  described  in 


CELESTIAL   MECHANICS 


277 


successive  seconds)  are  all  equal;  then,  wherever  0  may  be,  the 
triangles  AOB,  BOC,  COL,  etc.,  are  all  equal,  having  equal 
bases  and  the  common  vertex  0.  A  body  in  uniform  rectilinear 
motion  therefore  describes  with  its  radius  vector  equal  areas  in 
equal  times  around  any  point  whatever. 

Suppose,  now,  that  when  the  body  reaches  C  a  blow  or 
impulse  directed  towards  0  is  given,  imparting  a  velocity  which 
would  carry  it  to  K  in  one  second  if  it  had  been  at  rest  when 
struck.  The  resultant  of  the  original  motion  CL,  combined 
with  the  newly  imparted  motion  CK,  is  CD,  found  according  to 
the  "parallelogram  of  velocities"  (Physics,  p.  12)  by  drawing 
KD  and  LD  parallel,  respectively,  to  CL  and  CK,  so  that  at  the 
end  of  a  second  the  body  will 
arrive  at  D  instead  of  going  to 
L,  and  its  velocity  will  have 
become  CD  instead  of  BC. 

Now  the  area  of  the  tri- 
angle COD  equals  that  of 
COL,  because  they  have  the 
common  base  CO,  and  their 
vertices  are  on  a  line,  DL, 
parallel  to  that  base,  making 
their 
But 

COD=  COB.  It  follows, 
therefore,  that  when  a  moving  body  receives  an  impulse  directed 
towards  a  given  point  the  area  described  by  the  radius  vector  in  a 
second  around  that  point  remains  unchanged  by  that  impulse. 

If  the  impulse  had  been  directed  from  the  point  0,  towards 
K'  instead  of  K,  the  result  would  have  been  the  same.  The 
same  reasoning  shows  that  the  area  COD'  is  equal  to  COB. 

But  if  K  were  not  on  the  radius  vector  CO,  the  area  would 
be  changed,  increasing  if  CK  lay  between  CO  and  CL,  and 
decreasing  if  between  CO  and  CB. 


"altitude"    the    same. 
=  BOC-,   therefore 


FIG.  115 


directed 
towards  a 
point  does 
not  alter 
the  area 
described  by 
the  radius 
vector 
around 
that  point. 


278 


MANUAL   OF   ASTRONOMY 


Hence  fol- 
lows the 
general 
principle 
of  uniform 
description 
of  areas. 


Areal, 
linear,  and 
angular 
velocities 
denned. 


304.  Furthermore,  since  a  continuous  force,  like  attraction, 
directed  towards  or  from  a  fixed  center,  0,  may  be  regarded  as 
an  uninterrupted  succession  of  little  impulses,  each  directed 
along  the  radius  vector,  we  have  the  perfectly  general  law  that 
whenever  a  body  moves  under  the  sole  action  of  a  force  directed  along 
the  radius  vector  drawn  from  the  body  to  a  center,  the  radius  vector 
will  describe  around  that  center  areas  proportional  to  the  time.     It 

makes  no  difference  according  to  what 
law  the  intensity  of  the  force  varies: 
it  may  be  attractive  or  repulsive,  con~ 
tinuous  or  intermittent,  may  vary  as 
gravity  does  or  with  complete  irregu- 
larity; but  so  long  as  it  never  acts 
except  along  the  radius  vector  the 
"areal  velocity,"  as  it  is  called  (i.e., 
the  number  of  square  feet  or  acres  or 
square  miles  described  by  the  radius 
vector  in  a  unit  of  time),  remains 
absolutely  constant. 

Thus,  in  Fig.  116,  representing  part 
of  a  comet's  orbit  around  the  sun,  if  the  arcs  ab,  cd,  ef  are  each 
described  in  the  same  time,  then  the  shaded  areas  are  all  equal. 
The  converse  theorem  is  also  easily  proved,  viz.,  that  if  a 
body  moves  in  a  curve  in  such  a  way  that  its  radius  vector 
drawn  to  a  given  point  describes  equal  areas  in  equal  times 
around  that  point,  then  the  force  that  acts  upon  the  body  is 
always  directed  to  that  point. 

305.  Areal,  Linear,  and  Angular  Velocities.  —  Areal  velocity 
has  just  been  defined.      The  linear  velocity  of  a  body  is  the 
number  of  linear  units   (feet,   meters,  miles)  which  it  moves 
over  in- a  unit  of  time, — say  a  second.     Its  symbol  is  usually  V. 
The  angular  velocity  is  the  number  of  units  of  angle  (radians, 
degrees,  seconds)  swept  over  by  the  radius  vector  in  a  unit  of 
time.     The  usual  symbol  for  this  is  o>. 


FIG.  116.  — The  Law  of  Equal 
Areas 


m 


CELESTIAL   MECHANICS  279 

In  Fig.  117  if  AB  is  the  length  of  the  path  described  in  a 
unit  of  time,  AB  is  the  linear  velocity  V\  the  angle  ASB  is  the 
angular  velocity,  & ;  and  the  area  ASB  is  the  areal  velocity,  which 
is  constant.     Calling  this  A  and  regarding  the  sector  as  a  tri- 
angle (which  it  is  nearly  enough),  we  have  A  =  |  V  X  p,  p  being  Formula* 
the  line  Sb  drawn  from  the  center  of  force  perpendicular  to  the  for  lmear 
line  of  motion ;  so  that  if  we  regard  AB  as  the  base  of  the  velocities 
triangle,  p  is  its  altitude.     Hence,  we  have  the  equation  terms  of 

areal 
V  _  ^  A  _,  velocity. 

Also,  A  —  \  r^2  sin  ASB.  Since  in  a  second  of  time  the 
angle  ASB,  or  a>,  is  so  small  that  it  may  be  taken  equal  to  its 
sine,  and  ry2  equals  (sensibly)  r2,  we  have 

60  =  -^-  (2) 

In  every  case,  therefore,  of  motion  under  a  central  force, 
(1)  the  areal  velocity  (square  miles  per  second)  is  constant  in 
all  parts  of  the  orbit;  (2)  the  linear 
velocity  (miles  per  second)  varies  in- 
versely as  p,  the  perpendicular  drawn 
from  the  center  to  the  line  of  motion ; 
(3)  the   angular  velocity  (radians  or 
degrees  per  second)  varies  inversely 
as  the  square  of  the  radius  vector. 

These    three    statements    are    not  v  Extreme 

independent  laws,  but  simply  differ-      FIG.  117. -Linear  and  Angular     generality 
,    .      ,  .      ,  .  Velocities  of  the  laws. 

ent  geometrical  equivalents  for  one 

law.  They  hold  good  regardless  of  the  nature  of  the  force, 
requiring  only  that  when  it  acts  it  acts  directly  towards,  or  from, 
the  center,  along  the  line  of  the  radius  vector. 

306.   Circular  Motion.  —  In  the  special  case  when  the  path  of  Central  force 
a  body  is  a  circle  described  under  the  action  of  a  force  directed  m  case  of 

circular 

to  its  center,  both  the  linear  and  angular  velocities  are  constant,  motion. 


280 


MANUAL   OF   ASTRONOMY 


Kepler's 
laws  stated. 


Examples 
illustrating 
the  Har- 
monic Law. 


as  is  also  the  force,  which  is  given  by  the  familiar  formula 
already  several  times  used : 


772 
- 

r 


or 


obtained  by  substituting  for  V  in  equation  (a)  its  value,  2-Trr 
(the  circumference  of  the  circle),  divided  by  £,  the  time  of 
revolution.  As  the  orbits  of  the  principal  planets  are  all 
nearly  circular,  these  formulae  will  find  frequent  application. 

307.  Kepler's    Laws.  —  Early   in   the    seventeenth    century 
Kepler    discovered,    as    unexplained   facts,   three    laws    which 
govern  the  motions  of  the  planets, — laws  which  still  bear  his 
name.     He  worked  them  out  from  a  discussion  of  the  obser- 
vations which  Tycho  Brahe  had  made  through  many  preced- 
ing years  upon  the  planets,   Mars  especially.      They  are  as 
follows : 

(1)  The  orbit  of  each  planet  is  an  ellipse  with  the  sun  in  one 

(2)  The  radius  vector  of  each  planet  describes  equal  areas  in 
equal  times. 

(3)  The  squares  of  the  periods  of  the  planets  are  propor- 
tional to  the  cubes  of  their  mean  distances  from  the  sun;  i.e., 
tf:t^".'.a^'.a^.     This  is  the  so-called  "Harmonic  Law." 

308.  To  make  sure  that  the  student  apprehends  the  meaning  and  scope 
of  this  third  law,  we  add  a  few  simple  examples  of  its  application : 

1.  What  would  be  the  period  of  a  planet  having  a  mean  distance  from 
the  sun  of  one  hundred  astronomical  units,  i.e.,  a  distance  a  hundred  times 
that  of  the  earth  ? 

I8:1003  =  l2(year)  :  X*; 

whence,  X  (in  years)  =  VlOO3  =  1000  years. 

2.  What  would  be  the  distance  from  the  sun  of  a  planet  having  a 
period  of  125  years? 

I2(year)  :  1252  =  I3 :  Xs ;  whence  X  =  V1252  =  25  astron.  units. 


CELESTIAL  MECHANICS  281 

3.  What  would  be  the  period  of  a  satellite  revolving  close  to  the  earth's 

surface  ? 

(moon's  dist.)3  :  (dist.  of  satellite)8  =  (27.3  days)2:  Jt2, 

or,  603:13  =  27.32:J£2; 

27.3  days      1fcn^w 
whence,  X  = / J    =  Ih24m. 

V603 

The  Harmonic  Law  as  it  stands  in  Sec.  307  is  not  strictly  Modification 
true :  it  would  be  so  if  the  planets  were  mere  particles,  infini-  of  Harmonic 

r  Law  taking 

tesimal  as  compared  with  the  sun;  but  this  is  not  the  case,  account  of 
though  the  difference  is  so  slight  that  Kepler  did  not  detect  it.  Planets' 

r.    ,  masses. 

The  accurate  statement,  as  Newton  showed,  is 

t*  (M  +  Wl) :  t*  (M  +  mj  =  r^ :  r23, 

in  which  M  is  the  sun's  mass,  and  ml  and  ra2  are  the  masses  of 
the  two  planets  compared.  In  the  case  of  Jupiter  the  correc- 
tion makes  a  difference  of  about  two  days  in  its  period ;  i.e.,  its 
period  is  about  two  days  shorter  than  that  of  a  particle  moving 
in  the  same  orbit  would  be. 

309.  For  fifty  years  these  laws  remained  an  unexplained 
mystery.  Many  surmises,  partly  correct,  were  early  made  as 
to  their  physical  meaning.  Several  persons  "guessed"  that  the 
explanation  would  be  found  in  a  force  directed  to  the  sun; 
Newton  proved  it.  He  first  demonstrated  substantially,  as 
given  in  Sec.  303,  the  law  of  equal  areas  and  its  converse  as 
being  in  the  case  of  central  motion  a  necessary  consequence 
of  the  three  fundamental  laws  of  motion,  which  he  had  been  Newton 
the  first  to  formulate.  He  also  proved  by  a  demonstration  a  Provedthat 

*  .       the  law  of 

little  beyond  the  scope  of  this  book  that  if  a  planet  moves  in  gravitation 
an  ellipse  with  the  center  of  force  at  its  focus,  then  the  force  follows  from 
acting  upon  the  body  at  different  points  in  its  orbit  must  vary  iaws.    ' 
inversely  as  the  square  of  the  radius  vector  at  those  points;  and, 
finally,  he  proved  that,  granting  the  Harmonic  Law,  the  force 
from  planet  to  planet  must  also  vary  according  to  the  same  law 
of  inverse  squares. 


282 


MANUAL   OF   ASTRONOMY 


310.    For  circular  orbits   the  proof  is  very  simple.      From 
Demonstra-    equation  (b)  (Sec.  306)  we  have,  for  the  first  of  two  planets, 

tion  for 

circular  /"==  4  ?r2  —  ? 

orbits.  t^ 

in  which  /x  is  the  central  force  (measured  as  an  acceleration  in 
feet  per  second),  and  r^  and  ^  are,  respectively,  the  planet's 
distance  from  the  sun  and  its  periodic  time. 
For  a  second  planet,  „  2 

•F     =    4^212 


Dividing  the  first  equation  by  the  second,  we  get 


=  -^  X 


But,  by  Kepler's  third  law, 

t  2      r  3 
t* :  t22  =  r^ :  r£ ;  whence  -^  =  -2-. 

*i        ri 
t  2 
Substituting  this  value  of  -^  in  the  preceding  equation,  we  have 


Inferences 
from 
Kepler's 
laws  as  to 
the  force 
which  acts 
on  the 
planets. 


Gravitation 
depends 
upon  mass 
and  distance 


f         r          r  3        r  25 
/2        r2        M         rl 

i.e.,fi\f<i  =  r22:  rx2,  which  is  the  law  of  inverse  squares. 

In  the  case  of  elliptical  orbits  the  proposition  is  equally  true 
if  for  r  we  substitute  a,  the  semi-major  axis  of  the  orbit ;  but 
the  demonstration  is  much  more  complicated. 

311.  Inferences  from  Kepler's  Laws.  —  From  Kepler's  laws 
we  may  therefore  infer,  as  Newton  proved :  First  (from  the 
law  of  areas),  that  the  force  which  determines  the  orbits  of  the 
planets  is  directed  towards  the  sun. 

Second  (from  the  first  law),  that  the  force  which  acts  upon  any 
given  planet  varies  inversely,  at  different  points  in  the  orbit,  as  the 
square  of  the  radius  vector. 

Third  (from  the  Harmonic  Law),  that  the  force  which  acts 
upon  one  planet  is  the  same  that  it  would  be  for  any  other  planet 
put  in  the  place  of  the  first;  in  other  words,  the  attracting  force 


CELESTIAL  MECHANICS  283 

depends  only  on  the  mass  and  distance  of  the  bodies  concerned,  only,  and  is 

and  is  independent  of  their  physical  condition,  such  as  tempera-  fensibly 

ture,  chemical  constitution,  etc.     It  makes  no  difference  yet  Of  all  other 

detected  in  the  motion  of  a  planet  around  the  sun,  whether  it  circum- 
is  hot  or  cold,  made  of  hydrogen  or  of  iron;  but  it  would  be 
going  too  far  to  say  that  the  future  may  not  yet  show  some 
slight  differences  depending  upon  such  circumstances. 

312.   Newton's  Test  of  his  Theory  of  Gravitation  by  the  Motion  Test  of  the 

of  the  Moon.  —  When  Newton  first  conceived  the  idea  of  uni-  theory  °.f 

gravitation 

versal  gravitation  in  1665,  he  saw  at  once  that  the  moon's  by  means  of 
motion  around  the  earth  ought  to  furnish  a  test.     Since  the  themoon's 

motion. 

moon  s  distance  (as  was  well  known  even  then)  is  about  sixty 
times  the  radius  of  the  earth,  the  distance  it  should  fall  towards 
the  earth  in  a  second  ought  to  be,  if  his  idea  of  gravitation  was 

correct,  —  -,  or  ,  of  193  inches  (the  distance  which  a  body 

bO          obOO 

falls  in  a  second  at  the  earth's  surface),  provided  we  assume  Thedeflec- 
that  the  earth  attracts  as  if  its  mass  were  all  collected  at  its  tionof 

the  moon 

center,  —  to  prove    which   gave    Newton   much    trouble,    and  towards  the 
became  possible  only  after  his  invention  of  "fluxions."  earth  is  just 

what  it 

Now  g-gL-g-  of  193  inches  is  0.0535  inches.     Does  the  moon  should  be 


fall  towards  the  earth,  i.e.,  deflect  from  a  straight  line,  by  this  according  to 
amount  each  second? 

According  to  the  law  of  central  forces,  considering  the  moon's 

orbit  as  circular,  /  _  4   2       r 

J--         x  -, 

rt* 

and  the  deflection  is  one  half  of  this,  viz.,  Svr2^-      If  we  com- 

pute the  result,  making  r  =  238840  miles  reduced  to  inches, 
and  t  the  number  of  seconds  in  a  sidereal  month,  the  deflection 
comes  out  0.0534  inch,  a  difference  of  only  y-Q^-Q-jj  of  an  inch,  — 
practically  a  complete  accordance. 

Unfortunately  for  Newton,  when  he  first  made  this  test,  the  distance  of 
the  moon  in  miles  was  not  known,  because  the  size  of  the  earth  had  not 
then  been  determined  with  any  accuracy.  The  length  of  a  degree  was 


284 


MANUAL   OF   ASTRONOMY 


Why  the  supposed  to  be  about  60  miles  instead  of  69,  as  it  really  is.  Newton  corn- 
test  ap-  puted  the  radius  of  the  earth  on  this  erroneous  basis  and,  multiplying  it 
peared  tc  ^  ^  okt,ained  for  r,  the  distance  of  the  moon,  a  quantity  about  sixteen 
Newton  first  Per  cen^  to°  small;  from  this  he  calculated  a  corresponding  deflection  of 
applied  it.  only  about  0.044  inch.  The  discordance  between  this  and  0.0535  was  too 
great,  and  he  loyally  abandoned  the  theory  as  contradicted  by  facts. 

Six  years  later,  in  1671,  Picard's  measurement  of  an  arc  of  the  meridian 
in  France  corrected  the  error  in  the  size  of  the  earth,  and  Newton  on 
hearing  of  it  at  once  repeated  his  calculation,  or  tried  to,  for  the  story  goes 
that  he  was  too  excited  to  finish  it,  and  a.  friend  completed  it  for  him. 
The  accordance  was  now  satisfactory,  and  he  resumed  the  subject  with 
zeal  and  soon  established  the  correctness  of  his  theory. 


The  test  not 
sufficient  to 
demonstrate 
the  correct- 
ness of  the 
theory. 


Its  proof 
lies  in  its 
agreement 
with  all 
facts 
thus  far 
observed. 


The  inverse 
problem : 
to  determine 
what  the 
orbit  must 
be  if  the  law 
is  correct. 


It  is  to  be  noted  that  while  discordance  in  even  a  single  case 
would  be  fatal  to  the  theory,  accordance  in  a  single  case  does 
not  prove  it,  but  only  makes  it  more  or  less  probable.  The 
demonstration  of  the  law  of  gravitation  lies  in  its  entire  accord- 
ance, not  with  one  or  two  selected  facts,  but  with  a  countless 
multitude,  and  in  its  freedom  from  a  single  contradiction  shown 
by  the  most  refined  observations. 

Apparent  contradictions  have  now  and  then  cropped  out,  but 
all  have  found  explanation,  except,  perhaps,  one  slight  diver- 
gence at  present  outstanding  (in  the  motion  of  the  apsides  of 
the  planet  Mercury)  which  thus  far  baffles  the  mathematicians, 
but  will,  in  all  probability,  sooner  or  later  disappear  like  its 
predecessors. 

313.  The  Inverse  Problem.  —  Newton  did  not  rest  with  merely 
showing  that  the  motion  of  the  planets  and  of  the  moon  could 
be  explained  by  the  law  of  gravitation  ;  but  he  also  investigated 
and  solved  the  more  general  inverse  problem  and  determined 
what  kind  of  motion  is  necessary  according  to  that  law.  He 
found  that  the  orbit  of  a  body  moving  around  a  central  mass 
under  the  law  of  gravitation  need  not  be  a  circle,  nor  even  an 
ellipse  of  slight  eccentricity  like  the  planetary  orbits.  But  it 
must  be  a  Conic.  Whether  it  will  be  a  circle,  ellipse,  parabola, 
or  hyperbola  depends  on  circumstances. 


CELESTIAL   MECHANICS 


285 


314.  The  Conies.  —  (1)  The  ellipse  is  the  section  of  a  cone  The  two 
made  by  a  plane  which  cuts    completely  across  it,  as  EF  in  conics- 
Fig.  118.     The  ellipse  varies  in  form  and  size,  according  to  the 
position  and  inclination  of  the 
cutting  plane,   the   circle  being 
simply  a  special  case  when  the 
section  is  perpendicular  to  the 
axis  of  the  cone. 

(2)  The  Hyperbola.    When 
the  cutting  plane  makes  with  the 
axis    an   angle   less   than   BVC 
(the    semiangle    of  the    cone)    it 
plunges  continually  deeper  and 
deeper  into  the  cone  and  never 
comes  out  on  the  other  side.     The 
section  in  this  case  is  an  hyper- 
bola, GHK.     If  the  cutting  plane 
be  produced  upward,  it  encoun- 
ters the  other  nappe  of  the  cone 
(the  "cone  produced"),  cutting 
out  from  it  a  second  hyperbola, 
G'H'K',  exactly  like    the    first, 
but  turned  in  the  opposite  direc- 
tion.     The  pair  of  twin  curves, 
GHKsiud  G'H'K1,  are  considered 
as  two  parts  of  the  same  hyper- 
bola, the  axis  of  which,  HH'  in 
the  figure,  lies  between  the  two 
branches   and    outside    of   both, 

and  is  therefore  always  reckoned  as  negative.     The  center  of 
the  pair  of  twin  hyperbolas  is  the  middle  point  of  this  axis. 

(3)  The  Parabola.     When  the  cutting  plane  is  parallel  to  the 
side  of  the  cone,  as  PRO,  it  never  cuts  in  deeper,  nor,  on  the 
other  hand,  does  it  run  across  the  cone.     The  section  in  this 


FIG.  118.  — The  Conics 


286 


MANUAL   OF   ASTRONOMY 


The  parab- 
ola: the 
bounding 
curve 
between 
ellipses  and 
hyperbolas. 


case  is  called  a  parabola,  which,  so  to  speak,  is  the  boundary  or 
partition  between  the  ellipses  and  hyperbolas  which  can  be  cut 
from  a  given  cone  by  changing  the  inclination  of  a  given  plane. 
The  least  deflection  of  the  cutting  plane  outward  from  the 
parallel  changes  the  parabola  into  an  ellipse,  and  into  an  hyper- 
bola, if  inward. 


All  parab-  All  parabolas,  of  whatever  size,  and  cut  from  whatever  cone,  are  of  the 

olas  identi-     same  shape,  as  all  circles  are,  —  a  fact  by  no  means  obvious  without  demon- 

cal  in  form,     s^ratiOn,  though  we  cannot  give    the  proof  here.     This  does  not  mean, 

differing 

only  in  size. 


FIG.  110.— The  Relation  of  the  Conies  to  Each  Other 

however,  that  an  arc  of  one  parabola  is  of  the  same  shape  as  any  arc  of 
another  parabola  (taken  from  a  different  part  of  the  curve),  but  that  the 
complete  parabolas,  cut  out  from  infinitely  extended  cones,  are  all  similar, 
whether  the  cone  be  sharp  or  blunt,  or  whether  the  plane  cuts  it  near  to  or 
far  from  its  vertex. 


315,  The  Ellipse,  Parabola,  and  Hyperbola.  —  Fig.  119  shows 
the  appearance  and  relation  of  these  curves  as  drawn  upon  a 


The  ellipse, 
hyperbola, 
and  parabola 

compared  as  plane.     The  Ellipse  is  a  "  closed  curve     returning  into  itself, 

curves  upon    an(j  jn  ft  ^ne  sum  of  £ne  distances  of  any  point,  N,  from  the 

two  foci  equals  the  major  axis  ;  i.e.,  FN+  F'N  =  PA. 


CELESTIAL  MECHANICS  287 

The  Hyperbola  does  not  return  into  itself,  but  the  two 
branches  PN1  and  Pn"  go  off  into  infinity,  becoming  ultimately 
nearly  straight  and  diverging  from  each  other  at  a  definite  angle. 
In  the  hyperbola  the  difference  of  two  lines  drawn  from  any 
point  on  the  curve  to  the  two  foci  equals  the  major  axis;  i.e., 
F"N'  -  FN'  =  PA!,  C'P  being  the  semi-major  axis,  a,  of  the 
hyperbola. 

The  Parabola,  like  the  hyperbola,  fails  to  return  into  itself, 
but  its  two  branches,  instead  of  diverging,  become  more  and 
more  nearly  parallel.  It  has  but  one  accessible  focus  and  may 
be  regarded  either  as  an  ellipse  with  its  second  focus,  Ff, 
removed  to  an  infinite  distance,  and  therefore  having  an  infinite 
major  axis ;  or,  with  equal  correctness  it  may  be  considered  as 
an  hyperbola,  of  which  the  second  focus,  F",  is  pushed  indefi- 
nitely far  in  the  opposite  direction,  so  that  it  has  an  infinite 
(negative)  major  axis.  . 

In  the  ellipse  the  eccentricity  f  — — )  is  less  than  unity.  The  eccen- 

\"^/        /jrcr\  tricityof 

In  the  hyperbola  it  is  greater  than  unity  ( ).  ellipse  is 

\PC  J  less  than 

In  the  parabola  it  is  exactly  unity  ;  in  the  circle,  zero.  unity ;  that 

The  eccentricity  of  a  conic  determines  its  form.     All  parab-  ?gf  hfe^etg^°la 
olas,  therefore,  are  of  the  same  form,  as  already  said,  as  are  all  than  unity ; 
circles.     Of  ellipses  and  hyperbolas  there  is  an  infinite  variety  thatof 

J    parabola  is 

oi  forms,  irom  such  as  are  so  narrow  as  to  be  only  a  line  or  a  exactly 

pair  of  diverging  lines,  to  those  that  are  broad  as  compared  with  unity- 
their  length. 

316,   The  Problem  of  Two  Bodies.  —  This  problem,  proposed  The  problem 

and  completely  solved  by  Newton,  may  be  thus  stated :  °f  *wo 

Given  the  masses  of  two  spheres  and  their  positions  and  motions 

,    r  _  Motion  of 

at  any  moment ;  given  also  the  law  of  gravitation :  required  the  their  com. 
motion  of  the  bodies  ever  afterwards  and  the  data  necessary  to  mon  center 
compute  their  place  at  any  future  time.  unaffected 

The  mathematical  methods  by  which  the  problem  is  solved  by  their 
require  the  use  of  the  calculus  and  must  be  sought  in  works  on 


288  MANUAL   OF   ASTRONOMY 

analytical  mechanics  and  theoretical  astronomy,  but  the  general 
results  are  easily  understood. 

In  the  first  place,  the  motion  of  the  center  of  gravity  of  the  two 

bodies  is  not  in  the  least  affected  by  their  mutual  attraction. 

The  size  of         In  the  next  place,  the  two  bodies  will  describe  as  orbits  around 

orbits     their  common  center  of  gravity  two  curves  precisely  similar  in 

proportional  form,  but  of  size  inversely  proportional  to  their  masses,  the  form 

to  their         an(j  dimensions  of  the  two  orbits  being  determined  by  the  masses 

masses. 

and  velocities  of  the  two  bodies. 

If,   as  is   generally  the  case  in  the  solar  system,  the  two 

bodies  differ  greatly  in  mass,  it  is  convenient  to  ignore  the 
The  relative  center  of  gravity  entirely  and  to  consider  simply  the  relative 
orbit  of  the  motiOn  of  the  smaller  one  around  the  center  of  the  other,,  It 

smaller  with  .  .  ,  .  . 

respect  to  will  move  with  reference  to  that  point  precisely  as  11  its  own 
the  larger.  mass,  m,  had  been  added  to  the  principal  mass,  Jf,  while  it  had 
become  itself  a  mere  particle.  This  relative  orbit  will  be  pre- 
cisely like  the  orbit  which  m  actually  describes  around  the 
center  of  gravity,  except  that  it  will  be  magnified  in  the  ratio 
of  (M+  m)  to  M ;  i.e.,  if  the  mass  of  the  smaller  body  is  ^-^  of 
the  larger  one,  its  relative  orbit  around  M  will  be  just  one  per 
cent  larger  than  its  actual  orbit  around  the  common  center  of 
gravity  of  the  two. 

The  relative  317.  Finally,  the  orbit  will  always  be  a  "  conic,"  i.e.,  an 
orbit  a  conic,  en{p8e  Or  an  hyperbola;  but  which  of  the  two  it  will  be  depends 
anVsizTof  on  three  things,  viz.,  the  united  mass  of  the  two  bodies  (M  4-  m), 
which  de-  the  distance,  r,  between  m  and  M  at  the  initial  moment,  and  the 
thelassTs,  velocity,  V,  of  m  relative  to  M. 

their  initial        If  this  velocity,  V,  be  less  than  a  certain  critical  velocity,  U, 
andveioci-     wn^cn  depends  only  on  (M +  m}  and  r  and  is  called  the  "para- 
ties,  bolic  velocity"   or  "velocity  from  infinity,"  the  orbit  will  be 
an  ellipse;  if  greater,  it  will  be  an  hyperbola.     If,  however,  V 
and  U  should  happen  to  be  exactly  equal,  the  orbit  would  be  a 
Criterion  for  parabola ;  but  such  exact  equality  is  extremely  improbable,  — 
species.         the  chances  are  infinity  to  one  against  it. 


CELESTIAL   MECHANICS  289 

The  direction  of  the  motion  of  m  with  respect  to  M,  while  it  The  form 
has  influence  upon  the /ww  of  the  orbit  (its  "  eccentricity  "),  has  dePends 

J     ''  partly  upon 

nothing  to  do  with  determining  its  species  and  semi-major  axis  direction  of 
nor  with  its  period  in  case  the  orbit  is  elliptic  ;  these  are  all  inde-  initial 
pendent  of  the  direction  of  w's  motion. 

The  problem  is  completely  solved.  From  the  necessary  initial 
data  corresponding  to  a  given  moment  we  can  determine  the 
position  of  the  two  bodies  for  any  instant  in  the  eternal  past  or 
future,  provided  only  that  no  force  except  their  mutual  attraction 
acts  upon  them  in  the  time  covered  by  the  calculation. 

318.   The  Parabolic  Velocity. —  The  parabolic  velocity  at  the  Definition 
distance  r  is  also  called  the  "  velocity  from  infinity,"  because  it  °  the 
is  the  speed  which  would  be  acquired  by  the  particle  m  in  falling  velocity  or 
towards  the  mass  M  from  an  infinite  distance  to  the  distance  r  velocity 
from  M,  —  assuming,  of  course,  that  M  is  fixed  and  that  m  infinity, 
starts  from  rest  and  during  its  fall  is  not  acted  upon  by  any 
force  excepting  the  attraction  between  itself  and  M.     It  might 
be  supposed  that  this  velocity  would  be  infinite,  but  it  is  not  so 
unless  r  becomes  absolutely  zero.      It  is  given  by  the  formula 

j  _         / M  +  m  ,  IM  ,..  v  Formula 

ur  — /c\| -      »  or  simply  #\— '  for  the 

when  m  is  infinitesimal  as  compared  with  M.     (For  a  demon-  y^ocity.6 
stration  of  this  formula  the  reader  is  referred  to  works  on  ana- 
lytical mechanics.) 

In  this  formula  K  is  a  constant  which  depends  on  the  mass  of  M 
and  on  the  units  of  measurement  employed.  If  we  take  the  mass 
of  the  sun  as  the  unit  of  mass  and  the  radius  of  the  earth's  orbit  as 
the  unit  of  distance  for  r,  it  becomes  26.156  miles  per  second,  and 
we  have  for  the  parabolic  velocity  due  to  the  sun's  attraction  on  a 
particle  falling  from  infinity  to  the  distance  r,  /j 

Ur  (miles  per  second)  =  26.156  \-»         (2) 


and  Fr._  (2') 

1  Ur  signifies  "  parabolic  velocity  at  distance  r." 


290 


MANUAL   OF   ASTRONOMY 


Parabolic 
velocity  at 
surfaces  of 
sun,  earth, 
and  moon. 


If  the  mass  of  the  sun  were  four  times  as  great,  the  coeffi- 
cient would  be  doubled,  since,  according  to  equation  (1),  ?7  varies 
with  the  square  root  of  M.  At  a  distance  one  fourth  that  of 
the  earth  from  the  sun,  r  would  become  one  fourth  and  the 
parabolic  velocity  would  also  be  doubled.  At  the  distance  of 
Neptune,  where  r  =  30.05,  £7  is  only  4.77  miles  per  second. 

319.  Formula  (1)  enables  us  to  compute  the  parabolic  velocity  at  the  sur- 
face of  any  body  whose  mass  and  radius  are  known.  In  the  case  of  the  sun 

M  =  1  and  r  =  --  —  (i.e.,  433250  -f-  93  000000),  so  that  at  the  sun's  sur- 

face U=  383.2  miles  per  second  ;  if  a  body  were  ejected  from  the  sun  with 
a  speed  exceeding  this,  it  would  go  off  and  never  return. 

For  the  earth,  M  =  and  r  =  (Sec'  225)'  and  from  e<luar 


3320Q() 

tion  (1)  we  find  U  at  the  earth's  surface  equals  6.9  miles  per  second. 

At  the  surface  of  the  moon  a  similar  computation  gives  U  as  only 
1  .48  miles,  or  less  than  8000  feet  per  second.  A  body  projected  from  the 
moon  with  a  speed  greater  than  this  would  never  return,  and  it  will  be 
recalled  that  in  this  fact  probably  lies  the  explanation  why  the  moon  has 
lost  her  atmosphere. 


320,   Relation  between  the  Parabolic  Velocity  and  the  Nature 
of  the  Orbit  of  a  Body  revolving  around  the  Sun.  —  From  theo- 


Relation 
between  the 
parabolic 

velocity  and  retical  astronomy  (Watson,  p.  49)  we  have  the  equation 

the  species  ^ 

of  the  orbit.  a  =  LL  — ,  i 


a  being  the  semi-major  axis  of  the  orbit  of  a  body,  Vr  the  velocity 
of  the  body  in  its  orbit  at  a  point  whose  radius  vector  is  r,  and 
//,  a  constant  which  equals  \M&,  —  the  K  of  equation  (1).  From 
equation  (1),  MK?  =  r  X  £7.2,  so  that  ^  —  \r  U?.  Substituting  this 
value  of  fji  in  equation  (3),  we  find  at  once 

(4) 


The  semi-  This  equation  is  of  great  importance,  since  it  shows  that 

major  axis  ^  Specjes  of  the  orbit  is  determined  solely  by  the  difference 

of  orbit 

depends  between   U2  and  F2. 


CELESTIAL   MECHANICS  291 

If  the  denominator  of  the  fraction  is  positive,  the  value  of  a  upon  the 
will  be  positive  and  the  orbit  will  be  an  ellipse.      This  is  the  ^JjJJJ^ 
case  when  Fr,  the  orbital  velocity  at  the  distance  r,  is  less  than  and  F2  at 
Ur,  the  parabolic  velocity  at  that  distance.  distance  r. 

If,  on  the  other  hand,  Vr  is  greater  than  Ur,  the  denomi- 
nator becomes  negative,  and  so  does  «,  and  the  orbit  is  an 
hyperbola. 

If  Vr  exactly  equals  Ur,  the  denominator  becomes  zero,  a  becomes 
infinite,  and  the  orbit  is  a  parabola.  This  explains  why  U  is 
called  the  "parabolic  velocity":  at  every  distance  from  the 
sun  the  velocity  of  a  body  moving  in  a  parabola  is  precisely 
what  it  would  have  acquired  in  falling  to  that  point  from  an 
infinite  distance  under  the  sun's  attraction. 

If  the  orbit  is  an  ellipse,  the  velocity  at  every  point  in  the 
orbit  is  less  than  the  parabolic  velocity,  and  greater  if  the  orbit 
is  an  hyperbola.1 

In  order  that  a  planet  may  move  in  a  circle  around  the  sun,  Condition 
as  the  principal  planets  do  very  nearly,  a  must  equal  r,  and  equa-  [°rj^i* 
tion  (4),  by  substituting  r  in  place  of  a,  gives 
r  U2  U* 


whence,  F2  =  i  U2  and  F  =  Z/  =  0.7071  X  U;  i.e.,  the  velocity 
of  a  body  moving  in  a  circular  orbit  is  equal  to  the  parabolic 
velocity  multiplied  by  VJ. 

Vice  versa,  U—  vV%,  and  hence  the  parabolic  velocity  at 
distance  unity  (that  of  the  earth  from  the  sun)  equals  the  earth's 

1  The  expression  for  the  eccentricity  is  more  complicated  than  that  for  the 
semi-major  axis,  since  it  involves  the  angle  y  between  the  radius  vector  and  the 
tangent  drawn  at  its  extremity.  The  equation  is 


The  eccentricity  is  therefore  greater  than,  less  than,  or  equal  to  unity,  according 
as  (U2  —  V2)  is  positive  or  negative.  It  will  be  noticed  also  that  no  linear 
quantity  (r  or  a)  enters  into  the  expression,  which  determines  only  the  form 
and  not  the  size  of  the  orbit. 


292 


MANUAL   OF   ASTRONOMY 


Expression 
for  planet's 
period. 


Effect  of 
changes  of 
velocity 
upon  a 
body's 
orbit. 


Behavior  of 
the  frag- 
ments of  an 
exploded 
planet. 


orbital  velocity,  18.5  miles  X  V2  =  26.16  miles  per  second ;  and 
this  is  the  way  in  which  the  constant  K  is  usually  computed. 

321.  The  Expression  for  a  Planet's  Period.  —  From  theoret- 
ical astronomy  (Watson,  p.  46)  we  have  the  equation 

a* 


=  2-7TX 


(5) 


where  t  is  the  periodic  time.  This  embodies  Kepler's  third 
law,  and  shows  that  all  planets  moving  in  ellipses  and  having 
the  same  major  axis  will  have  the  same  period,  notwithstanding 
differences  in  the  eccentricity  of  their  orbits. 

Also  that  if  a  is  infinite,  as  in  the  parabola,  the  period  is 
also  infinite. 

Also  that  in  the  hyperbola  (in  which  a  is  negative)  the  period, 
since  it  involves  the  square  root  of  the  negative  quantity  a3,  is 
imaginary,  i.e.,  in  this  case  impossible. 

When  a  body  is  moving  in  a  parabola  ( F2  =  V2)  the  least 
decrease  of  F  by  a  disturbing  action  will  transform  the  orbit 
into  an  ellipse  with  a  definite  period,  or  an  increase  of  velocity 
will  make  it  an  hyperbola. 

Again,  if  a  planet  moving  in  a  circular  orbit  should  have 
its  speed  increased  in  a  ratio  greater  than  that  of  the  square 
root  of  2  to  1,  say  one  and  one-half  times,  it  would  go  off  in 
an  hyperbolic  arc  and  never  return. 

Finally,  if  a  planet  were  to  explode  at  any  point  in  its  orbit, 
all  the  pieces,  except  those  which  had  a  velocity  greater  than  the 
parabolic  velocity  at  the  point  of  explosion,  would  move  around 
the  sun  in  ellipses,  and  at  every  revolution  would  pass  through 
the  point  where  the  explosion  occurred ;  moreover,  any  frag- 
ments which  were  thrown  off  with  equal  velocities  would  have 
the  same  period  and  after  a  single  circuit  around  the  sun  would 
arrive  there  simultaneously. 


CELESTIAL  MECHANICS  293 


EXERCISES 

1.  Given  a  comet  moving  in  an  ellipse  with  the  eccentricity  0.5.     Com- 
pare the  velocities,  both  linear  and  angular,  at  the  perihelion  and  aphelion. 

(  Lin.  vel.  at  perihelion  is  three  times  that  at  aphelion. 
Am.    •<    . 

(  Ang.  vel.  "  "  nine      " 

2.  What  would  be  the  result  if  the  eccentricity  were  ^?    what  if  it 
were  f  ? 

]/      -3.  What  would  be  the  periodic  time  of  a  small  body  revolving  in  a  circle 
around  the  sun  close  to  its  surface  ?     (Apply  Kepler's  Harmonic  Law.) 

Ans.   2h47m.4:. 

l^     -  4.  What  would  be  its  velocity  ?  Ans.   270.8  miles  a  second. 

-»  5.  If  the  earth  had  a  satellite  with  a  period  of  8  months,  what  would  its 
distance  be?  Ans.    Four  times  that  of  the  moon. 

6.  If  Jupiter  were  reduced  to  a  mere  particle,  how  much  would  its 
period  be  lengthened?  (Consider  its  mass  to  be  ^fa  of  the  sun's,  and 
see  Sec.  308.) 

Solution.     Let  x  be  the  new  period  ;  then, 

x2  :  t2          =  r3  :  r3  =  1  :  1,  since  r  is  not  changed.     Whence, 

J.U4o 

X  =  t  \H  =  *  (!  +  i  *  To1?*  +  etc.)  =  t  (1  +  ^fo),  very  nearly. 

4SS2  6 
But  t  =  4332.6  days,  and  (x  -  t)  =  -^     '—  =  2.067  days.     Ans. 


7.  How  much  longer  would  the  earth's  period  be  if  it  were  a  mere 
particle?  Ans.  -5-5-^-3-3  of  a  year,  or  47.8  sec. 


8.  If  the  sun's  mass  were  a  hundred  times  greater,  what  would  be  the 
parabolic  velocity  at  the  earth's  distance  from  it  (Sec.  318)  ? 

Ans.    Ten  times  its  present  value,  i.e.,  261.6  miles  a  second. 

•*   9.  If  the  sun's  mass  were  reduced  50  per  cent,  what  would  be  the  para- 
bolic velocity  at  the  distance  of  the  earth?  Ans.    18.5  miles  a  second. 

10.  If  the  sun's  mass  were  to  be  suddenly  reduced  by  50  per  cent  or 
more,  what  would  be  the  effect  upon  the  now  practically  circular  orbits  of 
the  planets?  (See  Sec.  320,  last  paragraph.) 


294 


MANUAL   OF   ASTRONOMY 


11.  What  would  be  the  effect  upon  the  orbit  of  the  earth  if  the  sun's 
mass  were  suddenly  doubled  ? 

Ans.   It  would  immediately  become  an  eccentric  ellipse,  with  its 
aphelion  near  the  point  where  the  earth  was  when  the  change  occurred. 

12.  Let  Vr  be  the  velocity  in  an  orbit  at  a  point  where  the  radius  vector 
is  r,  and  let  Ur  and  UZa  be  the  parabolic  velocities  at  distances  r  and  2  a  from 
the  sun,  a  being  the  semi-major  axis  of  the  orbit.     Show  that 

y  2  —   77  2  4.    T  J     2 
V r     —   Ur     ±    U 2o  . 

The  plus  sign  applies  if  the  orbit  is  an  hyperbola,  the  minus  sign  if  it  is  an 
ellipse. 

In  words  this  may  be  stated  thus  (since  the  energy  of  a  moving  body  is 
proportional  to  the  square  of  its  velocity) : 

The  energy  of  a  body  moving  in  an  orbit  under  gravitation,  when  at  a  distance 
r  from  the  center  of  attraction,  equals  the  energy  it  would  have  acquired  by  falling 
to  r  from  infinity  ±  the  energy  it  would  have  acquired  by  falling  from  infinity 
to  the  distance  2  a,  the  major  axis  of  the  orbit. 


THE   PROBLEM  OF   THREE   BODIES:    PERTURBATIONS 
AND  THE   TIDES 

322.  As  has  been  said,  the  problem  of  two  bodies  is  completely 
solved ;  but  if  instead  of  two  spheres  attracting  each  other  we 
have  three  or  more,  the  general  problem  of  determining  their 
motions  and  predicting  their  positions  transcends  the  present 
power  of  human  mathematics. 

"The  problem  of  three  bodies"  is  in  itself  as  determinate  and 
capable  of  solution  as  that  of  two.  Given  the  initial  data,  i.e., 
the  masses,  positions,  and  motions  of  the  three  bodies  at  a  given 
instant;  then,  assuming  the  law  of  gravitation,  their  motions 
for  all  the  future  and  the  positions  they  will  occupy  at  any 
given  date  are  absolutely  predetermined.  The  difficulty  is  with 
our  mathematics. 

But  while  the  general  problem  of  three  bodies  is  intractable, 
nearly  all  the  particular  cases  of  it  which  arise  in  the  considera- 
tion of  the  motions  of  the  moon  and  of  the  planets  have  already 
been  practically  solved  by  special  devices,  Newton  himself 
leading  the  way;  and  the  strongest  proof  of  the  truth  of  the 


CELESTIAL  MECHANICS  295 

theory  of  gravitation  lies  in  the  fact  that  it  not  only  accounts 
for  the  regular  elliptic  motions  of  the  heavenly  bodies,  but 
also  for  their  apparent  irregularities. 

323,  It  is  quite  beyond  the  scope  of  this  work  to  discuss  the 
methods  by  which  we  can  determine  the  so-called  "  disturbing 
forces  "  and  the  effects  they  produce  upon  the  otherwise  elliptical 
motion  of  the  moon  or  of  a  planet.  We  make  only  two  or  three 
remarks. 

First,  that  the  "  disturbing  force  "  of  a  third  body  upon  two  Disturbing 
which  are  revolving  around  their  common  center  of  gravity  is  forc?  de~ 

0  pends  upon 

not  the  whole  attraction  of  the  third  body  upon  either  of  the  two,  the  differ- 
but  is  generally  only  a  small  component  of  that  attraction.     It  enceof 

5  J  _r  attractions 

depends  upon  the  difference  of  the  two  attractions  -exerted  by  the  Uponthe 
third  body  upon  each  of  the  pair  whose  relative  motions  it  disturbs,  bodies  dis- 

turbpd 

—  a  difference  either  in  intensity,  or  in  direction,  or  in  both. 

If,  for  instance,  the  sun  attracted  the  moon  and  earth  alike 
and  in  parallel  lines,  it  would  not  disturb  the  moon's  motion  Disturbing 
around  the  earth  in  the  slightest  degree,  however  powerful  its  force  of  sun 

r  upon  moon 

attraction  might  be.     The  sun  always  attracts  the  moon  more  only  one 


than  twice   as    powerfully  as   the  earth   does;    but  the   sun's 
disturbing  force  upon  the  moon  when  at  its  very  maximum  is  attraction. 
only  one  ninetieth  of  the  earth's  attraction. 

The  tyro  is  apt  to  be  puzzled  by  thinking  of  the  earth  as  fixed  while  the 
moon  revolves  around  it  ;  he  reasons,  therefore,  that  at  the  time  of  new 
moon,  when  the  moon  is  between  the  earth  and  sun,  the  sun  would  neces- 
sarily pull  her  away  from  us,  if  its  attraction  were  really  double  that  of  the 
earth  ;  and  it  would  do  so  if  the  earth  were  fixed.  We  must  think  of  the 
earth  and  moon  as  both  free  to  move,  like  chips  floating  on  water,  and  of 
the  sun  as  attracting  them  both  with  nearly  equal  power,  —  the  nearer  of 
the  two  a  little  more  strongly,  of  course. 

324,    Second,  it  is  only  by  a  mathematical  fiction  that  the  Disturbed 
"disturbed  body"  is  spoken  of  as  "moving  in  an  ellipse";  it  bodlesnevei 
never  does  so  exactly.     The  path  of  the  moon,  for  instance,  strictly  in 
never  returns  into  itself.  an  ellipse- 


296 


MANUAL   OF   ASTRONOMY 


Convenient 
fiction  of  the 
instantane- 
ous ellipse. 


Disturb- 
ances such 
only  techni- 
cally. 


Perturba- 
tions of 
moon  due 
solely  to 
the  sun. 


But  it  is  a  great  convenience  for  the  purposes  of  computation 
to  treat  the  subject  as  if  the  orbit  were  a  material  wire  always 
of  truly  elliptical  form,  having  the  moving  body  strung  upon  it 
like  a  bead,  this  "orbit"  being  continually  pulled  about  and 
changed  in  form  and  size  by  the  action  of  the  disturbing  forces, 
taking  the  body  with  it,  of  course,  in  all  these  changes.  This 
imaginary  orbit  at  any  moment  is  for  that  moment  a  true  instan- 
taneous ellipse  of  determinable  form  and  position,  but  is  con- 
stantly changing.  It  is  in  this  sense  that  we  speak  of  the 
eccentricity  of  the  moon's  orbit  as  continually  varying  and 
its  lines  of  apsides  and  nodes  as  revolving. 

The  student  must  be  careful,  however,  not  to  let  this  wire  theory  of 
orbits  get  so  strong  a  hold  upon  the  imagination  that  he  begins  to  think 
of  the  "orbits"  as  material  things,  liable  to  collision  and  damage.  An 
orbit  is  simply,  of  course,  the  path  of  a  body,  like  the  track  of  a  ship  upon 
the  ocean. 

325,  Third,  the  "disturbances"  and  "perturbations"  are  such 
only  in  a  technical  sense.     Elliptical  motion  is  no  more  natural 
or  proper  to  the  moon  or  to  a  planet  than  its  actual  motion  is; 
nor  in  a  philosophical  sense  is  the  pure  elliptical  motion  any 
more  regular   (i.e.,  "rule-following")  than  the  so-called  "dis- 
turbed" motion. 

We  make  the  remark  because  we  frequently  meet  the  notion  that  the 
"perturbations  "  of  the  heavenly  bodies  are  imperfections  and  blemishes  in 
the  system.  One  good  old  theologian  of  our  acquaintance  used  to  maintain 
that  they  were  a  consequence  of  the  fall  of  Adam. 

326.  Lunar  Perturbations.  —  The  sun  is  the  only  body  which 
sensibly  disturbs  the  moon ;  the  planets  are  too  small  and  too 
distant  to  produce  directly  any  effect  which  can  be  noticed, 
though  indirectly  by  their  effects  on  the  orbit  of  the  earth  they 
make  themselves  slightly  felt  —  at  second-hand,  so  to  speak. 

The  disturbing  force  due  to  the  solar  attraction  can  be  easily 
computed  at  any  moment  by  methods  indicated  in  the  General 


CELESTIAL   MECHANICS  297 

Astronomy,  but  we  shall  not  enter  into  that  subject.     This  Disturbing 
force  is  continually  changing  in  amount  and  direction,  and  the  force  easily 

J  computed. 

student  can  readily  understand  that  the  accurate  calculation  of  Computa- 
the  summed-up  effects  of  such  a  variable  force  in  changing  the  tion  of  its 
orbit  of  the  moon  and  her  place  in  the  orbit  must  be  extremely  plicated, 
difficult.     For  the  most  part,  however,  the  disturbances  are 
periodic,  running  through  their  phases  and  repeating  themselves 
at  regular  intervals,  so  that  they  can  be  expressed  by  trigono- 
metrical series.     Over  one  hundred  of  these  separate  "inequali- 
ties," as  they  are  called,  are  now  recognized  and  taken  account 
of  in  the  construction  of  the  Nautical  Almanac. 

We  mention  a  few  only  of  the  moon's  disturbances,  —  those 
which  are  largest  and  most  important,  two  or  three  of  which, 
especially  those  which  affect  the  time  of  eclipses,  were  discov- 
ered before  the  time  of  Newton,  though  not  explained. 

327.  Effect  on  the  Length  of  the  Month;  Revolution  of  the  Lengthening 
Line  of  Apsides;  Regression  of  the  Nodes.  — (1)  Effect  on  Length 
of  the  Month.  On  the  whole,  the  action  of  the  sun  tends  to 
lessen  the  effect  of  the  earth's  attraction  on  the  moon  by  about 
3-1--Q  part,  i.e.,  it  virtually  diminishes  //-  in  equation  (5)  (Sec.  321), 
and  this  increases  t,  the  period  or  length  of  the  month,  by  about 
yJ--0  part.  The  month  is  nearly  an  hour  longer  than  it  otherwise 
would  be  at  the  moon's  present  distance  from  the  earth. 

(2)  Revolution  of  the  Line  of  Apsides.     According  to  the  Advance  of 
"  age  "  of  the  moon  at  the  time  when  it  passes  the  perigee  or  aP8ldes- 
apogee,  the  sun  shifts  the  line  of  apsides  for  that  month,  some- 
times forward  (eastward)  and  sometimes  backward ;  but  in  the 

long  run  the  forward  motion  predominates,  and  the  line  moves 
eastward  and  completes  a  revolution  in  8.855  years. 

(3)  The  Regression  of  the  Nodes.     This    has    already  been  Regression 
repeatedly  mentioned.     Speaking  generally,  the  action  of  the  ofnodes- 
sun  on  the  whole  tends  to  draw  the  plane  of  the  moon's  orbit 
towards  the  ecliptic ;  but,  much  as  in  the  case  of  precession, 

the  effect  is  not  felt  in  any  permanent  change  of  the  inclination 


298 


MANUAL   OF   ASTRONOMY 


The 
evection. 


The  varia- 
tion. 


Annual 
equation. 


of  the  orbit,  but  shows  itself  in  a  westward  shifting  of  the  node, 
which  carries  it  around  once  in  18.6  years. 

328,  Periodic  Inequalities.  —  (4)  The  Evection.  This  is  an 
irregularity  which  at  the  maximum  puts  the  moon  forward  or 
backward  in  its  orbit  about  1J°,  and  has  for  its  period  about  one 
and  one-eighth  years,  the  time  required  for  the  sun  to  complete 
a  revolution  from  the  line  of  apsides  of  the  moon's  orbit  to  the 
same  line  again.  It  is  the  largest  of  the  moon's  periodic  pertur- 
bations and  was  discovered  by  Hipparchus  about  150  B.C.  It 
was  the  only  perturbation  known  to  the  ancients  and  may  affect 
the  time  of  an  eclipse  by  nearly  six  hours,  making  it  from  three 
hours  early  to  three  hours  late. 

It  depends  upon  an  alternate  increase  and  decrease  of  the  eccen- 
tricity of  the  moon's  orbit,  which  is  always  a  maximum  when  the 
sun  is  passing  the  line  of  apsides,  and  a  minimum  when  half- 
way between  them. 

(5)  The  Variation.     This  is  an  inequality  with  a  period  of 
one  synodic  month  and  reaches  its  maximum  of  about  40'  at  the 
octants,  i.e.,  the  points  45°  from  new  and  full  moon.     At  the 
octants  following  the  new  and  full  the  moon  is  about  Ih20m 
ahead  of  time,  and  at  the  octants  preceding  as  much  behind  time. 

This  inequality  was  detected  by  Tycho  Brahe  about  1580, 
though  there  is  some  reason  to  suppose  that  it  had  been  dis- 
covered some  five  hundred  years  before  by  an  Arabian  astrono- 
mer (Aboul  Wefa)  and  lost  sight  of.  It  becomes  zero  at  the  full 
and  new  moon,  and  therefore  does  not  affect  the  time  of  eclipses. 
For  this  reason  it  was  missed  by  the  Greek  astronomers. 

(6)  The  Annual  Equation.     This  is  the  one  remaining  ine- 
quality which  affects  the  moon's  place  by  an  amount  percep- 
tible to  the  naked  eye.     At  the  maximum  it  is  about  11',  with 
a  period  of  one  "anomalistic  year"  (Sec.  182). 

It  depends  upon  the  fact  that  when  the  earth  is  nearest  the 
sun,  in  January,  the  sun's  disturbing  effect  on  the  moon  is 
greater  than  the  average,  and  the  month  is  lengthened  a  little 


CELESTIAL  MECHANICS  299 

more  than  usual ;  and  vice  versa  when  the  sun  is  most  distant, 
in  July.  For  half  the  year,  therefore,  from  October  to  April, 
the  moon  keeps  falling  behind,  while  in  the  other  half  of  the 
year  the  month  is  slightly  shortened  and  the  moon  gains. 

For  more  detailed  geometrical  explanations  the  student  is  referred  to 
the  General  Astronomy  and  to  Herschel's  Outlines  of  Astronomy,  or  to  works 
on  celestial  mechanics  for  their  analytical  discussion. 

329.  The  Secular  Acceleration  of  the  Moon's  Mean  Motion.  —  Secular 
Among  the  multitude  of  lesser  inequalities  of  the  moon's  motion  acceler- 
this  is  of  special  interest  theoretically  and  is  still  in  some  respects 
a  "  bone  of  contention  "  among  astronomers.  It  was  discovered 
by  Halley  about  two  hundred  years  ago.  From  a  comparison 
of  ancient  with  modern  eclipses,  he  found  that  the  month  is  now 
certainly  shorter  than  it  was  in  the  days  of  Ptolemy,  and  that 
the  shortening  has  been  progressive,  the  moon  at  present  being 
about  a  degree,  or  two  hours  in  time,  in  advance  of  the  position 
it  would  occupy  if  it  had  kept  its  motion  unchanged  since  the 
Christian  era.  So  far  as  astronomers  could  see  at  the  time  of 
the  discovery,  the  process  would  continue  indefinitely, — in  secula 
seculorum  ;  hence  the  name. 

Laplace  about  1800  showed  that  this  effect  can  be  traced  to 
the  change  in  the  eccentricity  of  the  earth's  orbit,  which  is  at 
present  diminishing  (Sec.  164).     Since  the  major  axis  remains 
unaffected,  decrease  of  eccentricity  implies  an  increase  of  the  its  cause 
breadth  (minor  axis)  of  the  ellipse,  of  its  area  also,  and  therefore  j^™11 
of  the  average  distance  of  the  earth  from  the  sun  during  the  eccentricity 
year.     From  this  increased  distance  between  earth  and  sun  fol-  of  *Jj® 

J  ,       .  .         earth's 

lows  a  decreased  lengthening  of  the  month  by  the  sun's  disturbing  orbit 
action  (Sec.  327).    This  practically  amounts  to  the  shortening  of 
the  month,  which  shortening  will  continue  as  long  as  the  eccen- 
tricity of  the  earth's  orbit  continues  to  diminish,  —  about  24000 
years,  when  the  effect  will  cease  and  be  reversed. 

The  theoretical  amount  of  this  acceleration  of  the  moon's 
mean  motion  is  about  6"  in  a  century,  while  the  actual  value, 


300 


MANtJAL   OF   ASTRONOMY 


according  to  different  estimates  depending  on  comparison  of 
modern  with  the  much  less  accurate  ancient  observations,  is  decid- 
edly larger,  —  8".09,  according  to  Stockwell.  The  discrepancy 
is  now  generally  ascribed  to  a  slight  lengthening  of  the  day, 
diminishing  the  number  of  seconds  in  a  month  and  so  making 
the  month  apparently  shorter,  as  containing  a  smaller  number 
of  seconds.  Such  a  lengthening  of  the  day  could  be  accounted 
for  by  a  retardation  of  the  earth's  rotation  due  to  the  friction  of 
the  tides  (Sec.  345),  but  the  actual  difference  which  ought  to  be 
ascribed  to  this  action  is  as  yet  very  uncertain. 

For  an  excellent  non-technical  account  of  the  matter,  see  Newcomb's 
Popular  Astronomy,  p.  292. 

330.  The  Tides.  —  Just  as  the  disturbing  force  of  the  sun 
modifies  the  intensity  and  direction  of  the  earth's  attraction  on 
the  moon,  so  the  disturbing  forces  due  to  the  attractions  of  the  sun 
and  moon  act  upon  the  liquid  portions  of  the  earth  to  modify 
the  intensity  and  direction  of  gravity  and  generate  the  tides. 

These  consist  in  a  regular  rise  and  fall  of  the  ocean  surface, 
generally  twice  a  day,  the  average  interval  between  correspond- 
ing high  waters  on  successive  days  at  any  given  place  being 
24h51m.  This  is  precisely  the  same  as  the  average  interval 
between  two  successive  passages  of  the  moon  across  the  meridian, 
and  the  coincidence,  maintained  indefinitely,  makes  it  certain 
that  there  must  be  some  causal  connection  between  the  moon 
and  the  tides;  as  some  one  has  said,  the  odd  fifty-one  minutes 


Evidence 
that  they 
are  mainly 

due  to  action  is  "the  moon  s  earmark. 

of  the  moon. 


That  the  moon  is  largely  responsible  for  the  tides  is  also  shown 
by  the  fact  that  when  the  moon  is  in  perigee,  i.e.,  at  the  nearest 
point  to  the  earth,  they  are  nearly  twenty  per  cent  higher  than 
when  she  is  in  apogee.  The  highest  tides  of  all  happen  when 
the  new  or  full  moon  occurs  at  the  time  when  the  moon  is  in 
perigee,  especially  if  this  perigeal  new  or  full  moon  occurs  about 
the  first  of  January,  when  the  earth  is  also  nearest  to  the  sun* 


CELESTIAL   MECHANICS  301 

331.  Definitions.  —  While  the  water  is  rising  it  is  ^00^-tide ;  Definition 
when  falling  it  is  ebb.     It  is  high  water  at  the  moment  when  ofterms 

connected 

the  water-level  is  highest,  and  low  water  when  it  is  lowest.    The  With  the 
spring-tides  are  the  largest  tides  of  the  month,  which  occur  near  tides; 
the  times  of  new  and  full  moon,  while  the  neap  tides  are  the  neap  tides, 
smallest  and  occur  at  half -moon,  the  relative  heights  of  spring 
and  neap  tides  being  about  as  7  to  3. 

At  the  time  of  the  spring-tides  the  interval  between  the  cor- 
responding tides  of  successive  days  is  less  than  the  average,  Priming  and 
being  only  about  24h38m  (instead  of  24h51m),  and  then  the  tides 
are  said  to  prime.     At  the  neap 
tides  the  interval  is  greater  than 
the  mean,  —  about  25h6m,  —  and 
the  tide  lags. 

The  establishment  of  a  port  is 
the  mean  interval  between  the 
time  of  high  water  at  that  port 
and  the  next  preceding  passage  FIG.  120. -The  Tides 

of  the  moon  across  the  meridian. 

The  "establishment"   of  New  York,   for  instance,   is   8h13m;  The  estab- 
i.e.,  on  the  average,  high  water  occurs  8h13m  after  the  moon  lishment- 
has  passed  the  meridian;  but  the  actual  interval  varies  fully 
half  an  hour  on  each  side   of   this   mean  value    at   different 
times    of   the    month,    and   under   varying   conditions    of   the 
weather. 

332.  The  Tide-Raising   Force.  —  If   we  consider  the   moon  The  tide- 
alone,  it  appears  that  the  effect  of  her  attraction  upon  the  earth,  ™l*m% 
regarded  as  a  liquid  globe,  is  a  tendency  to  distort  the  sphere 

into  a  slightly  lemon-shaped  form,  with  its  long  diameter  point- 
ing to  the  moon,  raising  the  level  of  the  water  about  £  feet,  both 
directly  under  the  moon  and  on  the  opposite  side  of  the  earth 
(at  A  and  B,  Fig.  120),  and  very  slightly  depressing  it  on  the 
whole  great  circle  which  lies  half-way  between  A  and  B.  D  and 
E  are  two  points  on  this  circle  of  depression, 


302 


MANUAL   OF   ASTRONOMY 


Why  tide  is 
raised  on 
side  opposite 
the  moon. 


The  earth 
not  fixed 
while  at- 
tracted hy 
moon. 


Why  gravity 
is  dimin- 
ished both 
under  moon 
and  on 
opposite 
side  of 
earth. 


Students  seldom  find  any  difficulty  in  seeing  that  the  moon's 
attraction  ought  to  raise  the  level  at  A ;  but  they  often  do  find 
it  very  hard  to  understand  why  the  level  should  also  be  raised 
at  B.  It  seems  to  them  that  it  ought  to  be  more  depressed  just 
there  than  anywhere  else.  The  mystery  to  them  is  how  the 
moon,  when  directly  underfoot,  can  exert  a  lifting  force  such  as 
would  diminish  one's  weight. 

The  trouble  is  that  the  student  thinks  of  the  solid  part  of  the 
earth  as  fixed  with  reference  to  the  moon,  and  the  water  alone 
as  free  to  move.  If  this  were  the  case,  he 
would  be  entirely  right  in  supposing  that  at  B 
gravity  would  be  increased  by  the  earth's  attrac- 
tion instead  of  diminished;  the  earth,  however, 
is  not  fixed,  but  perfectly  free  to  move. 

333.  Explanation  of  the  Diminution  of  Gravity 
at  the  Point  opposite  the  Moon.  —  Consider  three 
particles  (Fig.  121)  at  B,  C,  and  A,  moving  with 
equal  velocities,  A  a,  Bb,  and  Cc,  but  under  the 
action  of  the  moon,  which  attracts  A  more 
powerfully  than  C  and  B  less  so.  Then,  if  the 
particles  have  no  bond  of  connection,  at  the  end 
of  a  unit  of  time  they  will  be  at  B1,  Cr,  and  A', 
having  followed  the  curved  paths  indicated.  But 
since  A  is  nearest  the  moon,  its  path  will  be  the  most  curved  of  the 
three,  and  that  of  B  the  least  curved.  It  is  obvious,  therefore, 
that  the  distances  of  both  B  and  A.  from  C  will  have  been  increased; 
and  if  they  were  connected  to  C  by  an  elastic  cord,  the  cord  would 
be  stretched,  both  A  and  B  being  relatively  pulled  away  from  C 
by  practically  the  same  amount.  We  say  relatively,  because  C  is 
really  pulled  away  from  B,  rather  than  B  from  C,  —  C  being 
more  attracted  by  the  moon  than  B  is ;  but  the  moon's  attraction 
tends  to  separate  the  two  all  the  same,  and  that  is  the  point. 

334.  The  Amount  of  the  Moon's  Tide-Raising  Force.  — When 
the  moon  is  either  in  the  zenith  or  nadir  the  weight  of  a  body 


Tide-Raising  Force 


CELESTIAL   MECHANICS  303 

at  the  earth's  surface  is  diminished  by  about  one  part  in  eight  Gravity 
and  a  half  millions,  or  one  pound  in  4000  tons. 

At  a  point  which  has  the  moon  on  its  horizon  it  can  be  shown 
that  gravity  is  increased  by  just  half  as  much,  or  about  one 
seventeen  millionth. 

The  computation  of  the  moon's  lifting  force  at  A  and  B  (Fig.  120)  is 
as  follows  :  The  distance  of  the  moon  from  the  earth's  center  is  60  earth 
radii,  so  that  the  distances  from  A  and  B  are  59  and  61,  respectively.  The 
moon's  mass  is  about  -^  of  the  earth's.  Taking  g  for  the  force  of  gravity 
at  the  surface  of  the  earth,  we  have,  therefore,  attraction  of  moon  on 

A  =  ioTeP'  attraction  on  c  =80^60''  and  attraction  on  B  =  whv' 

From  this  we  find 


Several  attempts  have  been  made  within  the  last  twenty 
years  to  detect  this  variation  of  weight  by  direct  experiment, 
but  so  far  unsuccessfully.  The  variations  are  too  small. 

The  moon's  attraction  also  produces  everywhere,  except  at  Moon's 
A,  B,  D,  and  E  (Fig.  120),  a  tangential  force  which  urges  the 
particles  along  the  surface  towards  the  line  AB  and  powerfully 
cooperates  in  the  tide-making. 

335.  The  Sun's  Tide-Producing  Force.  —  The  sun  acts  pre- 
cisely as  the  moon  does,  but,  being  nearly  400  times  as  far 
away,1  its  tidal  action,  notwithstanding  its  enormous  mass,  is  Tidal  in- 
less  than  that  of  the  moon  in  the  proportion  of  5  to  11  (nearly).  ^ee°^of 
At  new  and  full  moon  the  tidal  forces  of  the  sun  and  moon  con-  about  five 
spire,  and  we  then  have  the  spring-tides,  while  at  quadrature  elevenths 

*  ,  that  of  the 

they  are  opposed,  and  we  get  the  neap  tides,  their  relative  heights  moon. 
being  as  (11  +  5)  to  (11  —  5),  or  8  to  3.     The  priming  and  lag- 
ging of  the  tides  (Sec.  331)  is  also  due  to  the  sun's  influence. 

336.  Condition    for    Permanent    Tides.  —  If  the  earth  were 
wholly  composed  of  water,  and  if   it  kept  always  the  same 

1  It  can  be  proved  that  the  "tide-producing  force  "  of  a  body  varies  inversely 
as  the  cube  of  its  distance,  and  directly  as  its  mass. 


304 


MANUAL  OF  ASTRONOMY 


Effect  of 

earth's 

rotation. 

Tide  crest 
under  the 
moon  when 
depth  of 
water  ex- 
ceeds about 
14  miles. 

Tide  crest 
at  equator 
90°  from 
moon  when 
depth  less 
than  14 
miles;  but 
tide  crest 
in  high  lati- 
tudes still 
under  moon. 

Belt  of 
eddying  cur- 
rents in 
intermediate 
latitudes. 

Circum- 
stances 
which  make 
pure  theory 
insufficient 
to  explain 
many  tidal 
phenomena. 


face  towards  the  moon  (as  the  moon  does  towards  the  earth), 
so  that  every  particle  on  the  earth's  surface  were  always  sub- 
jected to  the  same  disturbing  force  from  the  moon,  then,  leaving 
out  of  account  the  sun's  action  for  the  present,  a  permanent 
tide  would  be  raised  upon  the  earth,  as  indicated  in  Fig.  120. 
The  difference  between  the  level  at  A  and  D  would  in  this  case 
be  a  little  less  than  2  feet. 

337.  Effect  of  the  Earth's  Rotation.  —  Suppose,  now,  the  earth 
to  be  put  in  rotation.  Evidently  the  two  tide-waves  A  and  B 
would  travel  westward  with  a  velocity  tending,  if  possible, 
to  equal  the  speed  of  the  earth's  eastward  rotation,  —  about 
1000  miles  an  hour  at  the  equator.  The  sun's  action  would 
also  generate  similar  tides,  about  T5T  as  great,  and  at  different 
times  of  the  month  the  solar  and  lunar  systems  would  alter- 
nately reinforce  and  oppose  each  other,  producing  spring  and 
neap  tides. 

If  the  earth  were  covered  with  water  of  uniform  depth,  the 
tides  would  circulate  with  perfect  regularity ;  and  if  the  depth 
were  more  than  about  14  miles,  then,  according  to  Darwin l  (and 
considering  the  lunar  tide  alone)  the  tide  crests  would  keep 
always  under  the  moon,  i.e.,  exactly  on  the  line  joining  the  centers 
of  earth  and  moon.  If  the  depth  were  less,  the  tide  crests  on 
the  earth's  equator  ivould  follow  the  moon  at  an  angle  of  90°,  giv- 
ing high  water  exactly  where  low  water  fell  in  the  deeper  ocean. 
In  high  latitudes,  where  the  earth's  rotation  is  slower,  the  tide 
crests  would  still  keep  under  the  moon ;  and  in  some  inter- 
mediate latitude  there  would  be  a  belt  of  eddying  currents  with 
no  regular  tidal  rise  and  fall. 

But  remembering  the  comparative  shallowness  of  the  oceans, 
the  great  variations  of  depth,  the  irregular  contour  of  the  shores, 
and  the  fact  that  the  American  continents  with  the  Antarctic 
interpose  a  barrier  almost  complete  from  pole  to  pole,  it  is 

1  We  simply  state  Professor  Darwin's  results.  For  details  and  discussion 
the  reader  is  referred  to  his  book,  The  Tides  (Houghton,  Mifflin  &  Co.). 


CELESTIAL  MECHANICS  305 

evident  that  the  whole  combination  of  circumstances  makes  it 
quite  impossible  to  determine  by  theory  what  the  course  and 
character  of  the  tide-waves  must  be.  We  are  obliged  to  depend 
upon  observations,  and  observations  are  more  or  less  inadequate, 
because,  with  the  exception  of  a  few  islands,  our  only  possible 
tide  stations  are  on  the  shores  of  continents  where  local  circum- 
stances largely  control  the  phenomena. 

338.  Free   and  Forced  Oscillations.  —  If   the   water   of   the 

ocean  is  suddenly  disturbed,  as,  for  instance,  by  an  earthquake,  Free  waves 
and  then  left  to  itself,  a  "  free  wave  "  is  formed,  which,  if  the  m  the 

'  '          m         ocean; 

horizontal  dimensions  of  the  wave  are  large  as  compared  with  their 
the  depth  of  the  water,  will  travel  at  a  rate  depending  solely  on  velocity- 
the  depth. 

Its  velocity  is  equal,  as  can  be  proved,  to  the  velocity  acquired 
by  a  body  in  falling  through  half  the  depth  of  the  ocean ;  i.e., 
v  =  ^Tgh,  where  h  is  the  depth  of  the  water. 

Observations  upon  waves  caused  by  certain  earthquakes  in  South 
America  and  Japan  have  thus  informed  us  that  between  the  coasts  of 
those  countries  the  Pacific  averages  between  2£  and  3  miles  in  depth. 

Now,  as  the  moon  in  its  apparent  diurnal  motion  passes  across 
the  American  continent  each  day  and  comes  over  the  Pacific 
Ocean,  it  starts  such  a  "parent"  wave  in  the  Pacific,  and  a 
second  one  twelve  hours  later.  These  waves,  once  started, 
move  on  nearly  (but  not  exactly)  like  a  free  earthquake  wave, 
—  not  exactly,  because  the  velocity  of  the  earth's  rotation  being 
about  1050  miles  an  hour  at  the  equator,  the  moon  moves 
(relatively)  westward  faster  than  the  wave  can  naturally  follow 
it,  and  so  for  a  while  the  moon  slightly  accelerates  the  wave. 
The  tidal  wave  is  thus,  in  its  origin,  a  "forced  oscillation";  in 
its  subsequent  travel  it  is  very  nearly,  but  not  entirely,  "  free." 

339.  Cotidal  Lines.  —  Cotidal  lines  are  lines  drawn  upon  the  Cotidai  lines 
surface  of  the  ocean  connecting  points  which  have  their  high  d 

water  at  the  same  moment  of  Greenwich  time.     They  mark  the 


306 


MANUAL   OF   ASTRONOMY- 


crest  of  the  tide- wave  for  every  hour,  and  if  we  could  map  them 
with  certainty,  we  should  have  all  necessary  information  as  to 
the  actual  motion  of  the  tide-wave. 

Unfortunately  we  can  get  no  direct  knowledge  as  to  the  posi- 
tion of  these  lines  in  mid  ocean ;  we  can  only  determine  a  few 
points  here  and  there  on  the  coasts  and  on  the  islands,  so  that 
much  is  necessarily  left  to  conjecture.  Fig.  122  is  a  reduced 
copy  of  a  cotidal  map,  borrowed  by  permission,  with  some  modi- 
fications, from  Guyot's  Physical  Geography. 

340.  Course  of  Travel  of  the  Tidal  Wave.  —  In  studying  this  map  we 
find  that  the  main  or  "  parent "  wave  starts  twice  a  day  in  the  Pacific,  off 
Callao,  on  the  coast  of  South  America.  This  is  shown  on  the  chart  by  a 
sort  of  oval  "  eye  "  in  the  cotidal  lines,  just  as  on  a  topographical  chart  the 
summit  of  a  mountain  is  indicated  by  an  eye  in  the  contour  lines.  From 
this  point  the  wave  travels  northwest  through  the  deep  water  of  the  Pacific 
at  the  rate  of  about  850  miles  an  hour,  reaching  Kamchatka  in  ten  hours. 
Through  the  shallower  water  to  the  west  and  southwest  the  velocity  is  only 
from  400  to  600  miles  an  hour,  so  that  the  wave  arrives  at  New  Zealand 
about  twelve  hours  old.  Passing  on  by  Australia  and  combining  with  the 
small  wave  which  the  moon  raises  directly  in  the  Indian  Ocean,  the  result- 
ant tide  crest  reaches  the  Cape  of  Good  Hope  in  about  twenty-nine  hours 
and  enters  the  Atlantic. 

Here  it  combines  with  a  smaller  tide-wave,  twelve  hours  younger,  which 
has  backed  into  the  Atlantic  around  Cape  Horn,  and  it  is  also  modified 
by  the  direct  tide  produced  by  the  moon's  action  upon  the  Atlantic.  The 
tide  resulting  from  the  combination  of  these  three  then  travels  northward 
through  the  Atlantic  at  the  rate  of  nearly  700  miles  an  hour.  It  is  about 
forty  hours  old,  reckoning  from  the  birth  of  its  principal  component  in 
the  Pacific,  when  it  first  reaches  the  coast  of  the  United  States  in  Florida ; 
and  our  coast  is  so  situated  that  it  arrives  at  all  the  principal  ports  within 
two  or  three  hours  of  that  time.  It  is  forty-one  or  forty- two  hours  old 
when  it  reaches  New  York  and  Boston. 

To  reach  London  it  has  to  travel  around  the  northern  end  of  Scotland 
and  through  the  North  Sea,  and  is  nearly  sixty  hours  old  when  it  arrives 
at  that  port  and  at  the  ports  of  the  German  Ocean. 

In  the  great  oceans  there  are  thus  three  or  four  tide  crests  traveling 
simultaneously,  following  each  other  nearly  in  the  same  track,  but  with 
continual  minor  changes.  If  we  take  into  account  the  tides  in  rivers  and 


CELESTIAL  MECHANICS 


307 


3 i 


3      8       g        5         g          § 


S §        ° 


2       §       §       3         g          g 


308 


MANUAL  OF   ASTRONOMY 


Speed  and 
limit  of 
ascent  of 
tides  in 
rivers. 


Height  of 
tides  in  mid 
ocean  and 
near  shore. 


Maximum 
height  of 
tides. 


sounds,  the  number  of  simultaneous  tide  crests  must  be  at  least  six  or 
seven  ;  i.e.,  the  tidal  wave  at  the  extremity  of  its  travel  (up  the  Amazon 
River,  for  instance)  must  be  at  least  three  or  four  days  old,  reckoned  from 
its  birth  in  the  Pacific. 

341.  Tides  in  Rivers.  —  The  tide- wave  ascends  a  river  at  a 
rate  which  depends  upon  the  depth  of  the  water,  the  amount 
of  friction,  and  the  swiftness  of  the  stream.  It  may,  and  gener- 
ally does,  ascend  until  it  comes  to  a  rapid  where  the  velocity  of 
the  current  is  greater  than  that  of  the  wave.  In  shallow  streams, 
however,  it  dies  out  earlier.  Contrary  to  what  is  usually  sup- 
posed, it  often  ascends  to  an  elevation  far  above  that  of  the  highest 
crest  of  the  tide-wave  at  the  river's  mouth.  In  the  La  Plata  and 
Amazon  it  goes  up  to  an  elevation  of  at  least  100  feet  above 


E 


Q 

r\ 


1 

A 


L 

r 


*    y   y 

FIG.  123.  —  Increase  in  Height  of  Tide  on  approaching  the  Shore 

the  sea-level.  The  velocity  of  the  tide-wave  in  a  river  seldom 
exceeds  10  or  20  miles  an  hour,  and  is  usually  much  less. 

342.  Height  of  Tides.  —  In  mid  ocean  the  difference  between 
high  and  low  water  is  usually  between  2  and  3  feet,  as  observed 
on  isolated  islands  in  deep  water ;  but  on  continental  shores  the 
height  is  ordinarily  much  greater.  As  soon  as  the  tide-wave 
"  touches  bottom,"  so  to  speak,  the  velocity  is  diminished,  the 
tide  crests  are  crowded  more  closely  together,  and  the  height 
of  the  wave  is  increased  somewhat  as  indicated  in  Fig.  123. 
Theoretically,  it  varies  inversely  as  the  fourth  root  of  the  depth  ; 
i.e.,  where  the  water  is  100  feet  deep  the  tide-wave  should  be 
twice  as  high  as  at  the  depth  of  1600  feet. 

Where  the  configuration  of  the  shore  forces  the  tide  into  a 
corner  it  sometimes  rises  very  high.  In  Minas  Basin,  near  the 
head  of  the  Bay  of  Fundy,  tides  of  70  feet  are  said  to  be  not 
uncommon,  and  some  of  nearly  100  feet  have  been  reported. 


CELESTIAL   MECHANICS  309 

343.  Effect  of  the  Wind  and  Changes  in  Barometric  Pressure.  —  When  the  Effect  of 
wind  blows  into  the  mouth  of  a  harbor,  it  drives  in  the  water  by  its  sur-  wind  and 
face  friction  and  may  raise  the  level  several  feet.     In  such  cases  the  time  chanSes  of 
of  high  water,  contrary  to  what  might  at  first  be   supposed,  is  delayed,  u  Qn  hej  ht 
sometimes  as  much  as  fifteen  or  twenty  minutes.     This  depends  upon  the  Of  tide  and 
fact  that  the  water  runs  into  the  harbor  for  a  longer  time  than  it  would  do  if  time  of  high 
the  wind  were  not  blowing.  water. 

When  the  wind  blows  out  of  the  harbor,  of  course  there  is  a  corre- 
sponding effect  in  the  opposite  direction. 

When  the  barometer  at  a  given  port  is  lower  than  usual,  the  level  of  the 
water  is  usually  higher  than  it  otherwise  would  be,  at  the  rate  of  about 
1  foot  for  every  inch  of  difference  between  the  average  and  actual  heights 
of  the  barometer. 

344.  Tides  in  Lakes  and  Inland  Seas.  —  These  are  small  and  difficult  to   Tides  in 
detect.     Theoretically,  the  range  between  high  and  low  water  in  a  land-  lakes. 
locked  sea  should  bear  about  the  same  ratio  to  the  rise  and  fall  of  tide 

in  mid  ocean  that  the  length  of  the  sea  does  to  the  diameter  of  the 
earth.  On  the  coasts  of  the  Mediterranean  the  tide  averages  less  than 
18  inches,  but  it  reaches  the  height  of  3  or  4  feet  at  the  head  of  some  of 
the  gulfs.  In  Lake  Michigan,  at  Chicago,  a  tide  of  about  If  inches  has 
been  detected,  the  "establishment"  (Sec.  331)  of  Chicago  being  about 
thirty  minutes. 

345.  Effects  of  the  Tides  on  the  Rotation  of  the  Earth.  —  If  Effect  of 
the  tidal  motion  consisted  merely  in  the  rising  and  falling  of  tldes  upon 
the  particles  of  the  ocean  to  the  extent  of  some  2  feet  twice  day. 
daily,  it  would  involve  a  very  trifling  expenditure  of  energy, 

and  this  is  the  case  with  the  mid-ocean  tide.  But  near  the  land 
this  slight  oscillatory  motion  is  transformed  into  the  bodily 
traveling  of  immense  masses  of  water,  which  flow  in  upon  the 
shallows  and  then  out  again  to  sea  with  a  great  amount  of  fluid 
friction,  and  this  involves  the  expenditure  of  a  very  consider- 
able amount  of  energy.  From  what  source  does  this  energy 


The  answer  is  that  it  must  be  derived  mainly  from  the  earth's 
energy  of  rotation,  and  the  necessary  effect  is  to  lessen  the  speed 
01  rotation  and  to  lengthen  the  day.  Compared  with  the  earth's 
whole  stock  of  rotational  energy,  however,  the  loss  by  tidal 


310 


MANUAL   OF   ASTRONOMY 


Counteract- 
ing causes. 


Effect  of 
tide  to  cause 
the  moon's 
distance  to 
increase  and 
to  lengthen 
the  month. 


Tidal 
avolution. 


friction  even  in  a  century  is  very  small  and  the  theoretical 
effect  on  the  length  of  the  day  extremely  slight.  Moreover, 
while  it  is  certain  that  the  tidal  friction,  by  itself  considered, 
lengthens  the  day,  it  does  not  follow  that  the  day  grows  longer. 
There  are  counteracting  causes,  —  for  instance,  the  earth's 
radiation  of  heat  into  space  and  the  consequent  shrinkage  of 
her  volume.  At  present  we  do  not  know  as  a  fact  whether  the 
day  is  really  longer  or  shorter  than  it  was  a  thousand  years 
ago.  The  change,  if  real,  cannot  well  be  as 

great  as  y-oVu"  °^  a  second. 

346.  Effect  of  the  Tide  on  the  Moon's 
Motion.  —  Not  only  does  the  tide  diminish 
the  earth's  energy  of  rotation  directly  by  the 
tidal  friction,  but  theoretically  it  also  com- 
municates a  minute  portion  of  that  energy  to 
the  moon.  It  will  be  seen  that  a  tidal  wave, 
situated  as  in  Fig.  124,  would  slightly  accel- 
erate the  moon's  motion,  the  attraction  of  the 
moon  by  the  tidal  protuberance,  F,  being 
slightly  greater  than  that  of  the  opposite  wave 
at  F .  This  difference  would  tend  to  draw  it 
along  in  its  orbit,  thus  slightly  increasing  its 
velocity,  and  so  indirectly  increasing  the  major 
axis  of  the  moon's  orbit  as  well  as  its  period. 
The  tendency  is,  therefore,  to  make  the 
moon  recede  from  the  earth  and  to  lengthen  the  month. 

Upon  this  interaction  between  the  tides  and  the  motions  of 
the  earth  and  moon  Prof.  George  Darwin  has  founded  his 
theory  of  tidal  evolution;  viz.,  that  the  satellites  of  a  planet, 
having  separated  from  it  millions  of  years  ago,  have  been  made 
to  recede  to  their  present  distances  by  just  such  an  action. 

An  excellent  popular  statement  of  this  theory  will  be  found  in  the 
closing  chapter  of  Sir  Robert  Ball's  Story  of  the  Heavens,  and  one  more 
complete,  but  still  popular,  in  his  Time  and  Tide. 


FIG.  124.  — Effect  of 
the  Tide  on  the 
Moon's  Motion 


CHAPTER  XII 
THE   PLANETS   IN   GENERAL 

Bode's  Law  —  The  Apparent  Motions  of  the  Planets  —  The  Elements  of  their  Orbits 
—  Determination  of  Periods  and  Distances  —  Perturbations,  Stability  of  the 
System  —  Data  referring  to  the  Planets  themselves  —  Determination  of  Diam- 
eter, Mass,  Rotation,  Surface  Peculiarities,  Atmosphere,  etc.  —  Herschel's  Illus- 
tration of  the  Scale  of  the  System 

347.   The  stars  preserve  their  relative  configurations,  however  stars 

much  they  may  alter  their  positions  in  the  sky  from  hour  to  sensibly 

hour.     The  Dipper  always  remains  a  "  dipper"  in  every  part  of  celestial 

the  diurnal  circuit.  sphere  ; 


But  certain  of  the  heavenly  bodies,  and  the  most  conspicuous 
of  them,  behave  differently.  The  sun  and  the  moon  move 
always  steadily  eastward  through  the  constellations  ;  and  a  few 
others,  which  look  like  brilliant  stars,  but  are  not  stars  at  all, 
creep  back  and  forth  among  the  star  groups  in  a  less  simple 
manner. 

These  moving  bodies  were  called  by  the  Greeks  Planets,  i.e., 
"  wanderers."  They  enumerated  seven,  —  the  Sun  and  Moon 
and,  in  addition,  Mercury,  Venus,  Mars,  Jupiter,  and  Saturn. 

348.   List  of  Planets.  —  At  present  the  sun  and  moon  are  not  List  of  the 
reckoned  as  planets  ;  but  the  number  of  others  known  to  the  Planets- 
ancients  has  been  increased  by  two  new  worlds,  —  Uranus  and 
Neptune,  of  great  magnitude,  though  inconspicuous  on  account 
of  their  distance,  —  besides  a  host  of  little  asteroids. 

The  list  of  the  principal  planets  in  their  order  of  distance 
from  the  Sun  stands  thus  at  present:  Mercury,  Venus,  the 
Earth,  Mars,  Jupiter,  Saturn,  Uranus,  and  Neptune. 

Moreover,  between  Mars  and  Jupiter,  where  there  is  a  wide  Asteroids 
gap  in  which  another  planet  would  naturally  be  looked  for,  andEros- 

311 


312 


MANUAL   OF   ASTRONOMY 


Planets  non- 
luminous. 


there  have  already  (October,  1909)  been  discovered  more  than 
seven  hundred  little  bodies  called  "asteroids,"  which  probably 
represent  a  single  planet,  somehow  "  spoiled  in  the  making," 
so  to  speak,  or  subsequently  burst  into  fragments. 

One  of  this  family,  Eros,  discovered  in  1898,  crosses  the 
inner  boundary  mentioned,  —  the  orbit  of  Mars,  —  and  at  times 
comes  nearer  to  the  earth  than  any  other  heavenly  body  except 
the  moon. 

The  planets  are  non-luminous  bodies  which  shine  only  by 
reflected  sunlight,  —  globes  which,  like  the  earth,  revolve 
around  the  sun  in  orbits  nearly  circular,  moving  all  of  them 
in  the  same  direction  and  (with  numerous  exceptions  among 
the  asteroids)  nearly  in  the  common  plane  of  the  ecliptic. 

All  but  the  inner  two  and  the  asteroids  are  attended  by 
satellites.  Of  these  the  Earth  has  one  ( the  moon),  Mars  two, 
Jupiter  eight,  Saturn  ten,  Uranus  four,  and  Neptune  one.  Four 
of  these  satellites  have  been  discovered  since  1900. 

349.  Relative  Distances  of  the  Planets  from  the  Sun;  Bode's 
Bode's  Law.  Law.  —  There  is  a  curious  approximate  relation  between  the 
distances  of  the  planets  from  the  sun,  usually  known  as  Bode's 
Law. 

It  is  this  :  Write  a  series  of  4's.  To  the  second  4  add  3 ;  to 
the  third  add  3  x  2,  or  6 ;  to  the  fourth,  4  x  3,  or  12  ;  and  so 
on,  doubling  the  added  number  each  time,  as  in  the  following 
scheme : 


Satellites. 


4 
3 

7 

9 

4 

6 
10 

0 

4 

12 
16 

i 

4 

24 

4 

48 
52 

4 
96 
100 

h 

4 
192 
196 

¥ 

4 

384 
388 

V 

[28] 
© 

The  resulting  numbers  (divided  by  10)  are  approximately 
No  satis-  equal  to  the  true  mean  distances  of  the  planets  from  the  sun, 
factory  expressed  in  radii  of  the  earth's  orbit  (astronomical  units)  — 

explanation 

of  the  law      excepting  Neptune,  however  ;  in  his  case  the  law  breaks  down 
yet  reached,   utterly.     For  the  present,  at  least,  it  must  therefore  be  regarded 


THE   PLANETS   IN   GENERAL 


313 


as  a  mere  coincidence  rather  than  a  real  "law,"  but  it  is  not 
unlikely  that  its  explanation  may  ultimately  be  found  when  the 
evolution  of  the  solar  system  comes  to  be  better  understood. 

It  is  known  as  Bode's  Law  because  first  brought  prominently  into  notice 
by  him  in  1772,  though  it  appears  to  have  been  discovered  by  Titius  of 
Wittenberg  some  years  earlier. 

350,    Table  of  Names,  Distances,  and  Periods 


NAME 

SYMBOL 

DISTANCE 

BODE 

DlFF. 

SID.  PERIOD 

SYN. 
PERIOD 

Mercury  .  .  . 
Venus  .... 
Earth  

$ 

9 

© 

0.387 
0.723 
1.000 

0.4 
0.7 
1.0 

-  0.013 
+  0.023 
0.000 

88d     or        3m 
224*.  7  or      7|m 
365|d  or  ly 

116* 
584d 

Mars  

# 

1.523 

1.6 

-  0.077 

687d     orlylO™ 

780d 

Mean  asteroid 

2.650 

2.8 

-0.150 

3y.l  to  8y.9 

various 

Jupiter  .... 
Saturn  .... 
Uranus  .... 

Neptune  .  .  . 

y 

h 

0  &  ¥ 

V 

5.202 
9.539 
19.183 
30.054 

5.2 
10.0 
19.6 
38.8 

+  0.002 
-  0.461 
-  0.417 
-  8.746 

lly.9 
29y.5 
84y.O 
164y.8 

399d 
378d 
370d 
36711 

Table  of 
the  planets-, 
symbols, 
distances, 
and  periods. 


The  column  headed  "Bode"  gives  the  distance  according  to  Bode's  Law; 
the  column  headed  "Diff.,"  the  difference  between  the  true  distance  and  that 
given  by  Bode's  Law. 


351,    Periods.  —  The  sidereal  period  of  a  planet  is  the  time  of  Definition  of 
its  revolution  around  the   sun,  from  a  star  to  the  same  star  Sldereal  and 

synodic 

again,  as  seen  from  the  sun.     The  synodic  period  is  the  time  periods. 
between  two  successive  conjunctions  of  the  planet  with  the  sun, 
as  seen  from  the  earth. 

The  sidereal  and  synodic  periods  are  connected  by  the  same 
relation  as  the  sidereal  and  synodic  months  (Sec.  191),  namely, 


_  =  ---  ,  in  which 

k        -L          & 


,  P,  and  S  are,  respectively,  the  periods  Equation 

expressing 

of  the  earth  and  of  the  planet,  and  the  planet's  synodic  period  ;   relation 

•*  .  between 

and  the  numerical  difference  between  —  and  —  is  to  be  taken    them> 

P          E 


314 


MANUAL   OF   ASTRONOMY 


without  regard  to  sign;  i.e.,  for  an  inferior  planet,  —  — ;  for 

111  S     P     E 

a  superior  one,  —  = • 

*  SEP 


FIG.  125.  —  The  Planetary  Orbits 

The  two  last  columns  of  the  table  of  Sec.   350   give  the 
approximate  periods,  both  sidereal  and  synodic,  for  the  different 
planets. 
Map  of  the       Fig.  125  shows  the  smaller  orbits  of  the  system  (including 

orbits*       the  orbit  of  JuPiter)>  drawn  to  scale,  the  radius  of  the  earth's 
orbit  being  taken  as  one  centimeter. 


THE  PLANETS  IN  GENERAL 


315 


Conjunction 


On  this  scale  the  diameter  of  Saturn's  orbit  would  be  19.08 
centimeters,  that  of  Uranus  38.36  centimeters,  and  that  of  Nep- 
tune 60.11  centimeters,  or  about  2  feet.  The  nearest  fixed  star, 
on  the  same  scale,  would  be  about  a  mile  and  a  quarter  away. 

It  will  be  seen  that  the  orbits  of  Mercury,  Mars,  Jupiter,  and 
several  of  the  asteroids  are  quite  distinctly  eccentric. 

352.  Explanation  of  Terms.  —  Fig.  126  illustrates  the  mean-  Technical 
ing  of  various  terms  used  in  describing  the  position  of  a  planet  Jf^18 
with  respect  to  the 
sun.  E  in  the  fig- 
ure is  the  position 
of  the  earth,  the 
inner  circle  is  the 
orbit  of  an  inferior 
planet  (Mercury  or 
Venus),  and  the 
outer  circle  is  that 
of  a  superior  planet, 
Mars,  for  instance. 

The  Elongation 
of  a  planet  is  the 
angle  at  the  earth 
between  lines 
drawn  from  the  ob- 
server to  the  planet 
and  to  the  sun, 

i.e.,  the  apparent  angular  distance  of  the  planet  from  the  sun; 
for  a  planet  at  P  it  is  the  angle  SEP. 

For  a  superior  planet  the  elongation  can  have  any  value  from 
0°  to  180°.  For  an  inferior  planet  there  is  a  certain  maxi- 
mum value,  called  the  greatest  elongation,  which  must  be  less 
than  90°.  This  greatest  elongation  is  the  angle  between  a  line 
drawn  from  the  earth  to  the  sun  and  another  line  drawn  tangent 
to  the  planet's  orbit,  —  the  angle  VES  in  the  figure. 


Opposition 
FIG.  126.  —  Planetary  Configurations  and  Aspects 


316  MANUAL   OF   ASTRONOMY 

Conjunc-  Absolute    Conjunction   occurs  when   the    elongation   of  the 

tion :  supe-     pianet  is  zero ;  superior  conjunction  when  the  planet  is  beyond 
inferior.        the  sun  ;  inferior  when  between  earth  and  sun,  —  a  position, 
of  course,  impossible  for  a   superior  planet.      Conjunction  in 
longitude  occurs  when  the  planet's  longitude  is  the  same  as  the 
sun's,  arid  in  right  ascension  when  it  has  the  same  right  ascen- 
sion as  the  sun. 
Opposition.         Opposition  occurs  when  the  elongation  of  a  planet  is  180° 

and  the  planet  rises  at  sunset. 

Quadrature.        Quadrature  occurs  when  the  planet  has  an  elongation  of  90°. 

An  inferior  planet  cannot  be  in  either  opposition  or  quadrature. 

The  astrologers  called  these  positions  ''aspects  "  and  recognized 

several  others,  —  for  instance,  "sextile,"  "trine,"  "  octant,"  etc. 

353.  Apparent  Motions  of  the  Planets.  —  If  we  imagine  our- 
selves looking  down  upon  the  orbits  perpendicularly  from  their 

Apparent       northern  side,  so  as  to  see  them  in  plan,  they  would  appear  as 
motion  of      snown  in  j^  ^25,  and  the  planets  would  travel  regularly  for- 

planets  com- 
plicated by     ward  (contrary  to  the  hands  of  a  watch)  with  a  steady,  almost 

earth's          uniform,  motion.     Viewed  from  the  earth,  however,  we  see  the 

motion. 

orbits  nearly  edgewise,  and  their  appa.rent  motions  are  compli- 
cated, being  made  up  of  their  own  real  motion  around  the  sun, 
combined  with  a  purely  apparent  motion  due  to  the  movement 
of  the  earth. 

Their  apparent  motion  as  seen  by  us  may  be  considered  under 
three  different  aspects : 

(1)  The  motion  in  space  relative  to  the  earth. 

(2)  The  motion  on  the  celestial  sphere  relative  to  the  constel- 
lations, i.e.,   change  of  right  ascension  and  declination  or  of 
celestial  latitude  and  longitude. 

(3)  With  reference  to  their  apparent  angular  distance  from 
the  sun,  i.e.,  motion  in  elongation. 

354.  Motion  in  Space  Relative  to  the  Earth.  —  The   funda- 
mental principle  of  relative  motion  is  that  if  we  look  at  a  body 
at  rest  while  we  ourselves  are  moving,  its  relative  motion,  i.e.,  the 


THE   PLANETS   IN   GENERAL 


317 


change  in  its  distance  and  direction  from  us,  will  be  the  same  as 
if  we  were  at  rest  and  it  possessed  our  motion  reversed.  If  we 
look  at  a  body  while  we  move  to  the  south,  it  appears  to  move 
towards  the  north.  If  we  approach  it,  the  effect  is  the  same  as 
if  it  were  coming  towards  us,  and  so  on. 

If  the  body  has  a  motion  of  its  own,  then  the  total  apparent 
or  relative  motion  will  be  the  resultant  of  its  real  motion  com- 
bined with  our  reversed  motion, 
according  to  the  law  of  compo- 
sition of  motions  (Physics, 
p.  18). 

A  planet  at  rest,  therefore, 
would  appear  to  move  in  an 
orbit  precisely  like  that  of  the 
earth  in  form  and  size  and  in 
the  same  plane,  always  keeping 
its  motion  opposed  to  our  own, 
though  going  around  this  ap- 
parent orbit  in  the  same  direc- 
tion as  the  earth  (just  as  any  FIG.  127. -Geocentric  Motion  of  Jupiter 
VJ  J  from  1708  to  1720 

two    opposite    points    on    the  After  Cassini 

circumference  of   a   revolving 

wheel  are  always  moving  in  opposite  directions,  though  going 
the  same  way  around  the  axis).  And  since  the  planets  are 
really  revolving  around  the  sun,  it  follows  that  their  apparent 
or  geocentric  motion  is  a  combination  of  two  motions,  —  that  of 
a  body  moving  once  a  year  around  the  circumference  of  a  circle1 
equal  to  the  earth's  orbit,  while  at  the  same  time  the  center  of 
that  circle  is  carried  around  the  sun  in  the  real  orbit  of  the 
planet,  and  in  the  same  period  with  the  planet.  Jupiter,  for 
instance,  appears  to  move  as  in  Fig.  127. 

This  is  the  orbit  we  should  find  if  we  were  to  attempt  to  map 
it  out  by  the  method  used  for  determining  the  form  of  the  orbit 

1  The  "circles "  spoken  of  here  are  strictly  ellipses  of  small  eccentricity. 


Relative 
motion  in 
space:  a 
combination 
of  the 
planet's 
real  motion 
with  that  of 
the  earth 
reversed. 


Result  an 
epicycloidal 
motion 
relative 
to  earth. 


318 


MANUAL   OF   ASTRONOMY 


Effect  of  the 
eccentricity 
of  the  real 
orbits. 


Planet's 
motion  on 
the  celestial 
sphere : 
alternately 
direct  and 
retrograde 
in  right 
ascension 
and  longi- 
tude. 


Stationary 
points. 


of  the  earth  around  the  sun  (Sec.  159),  i.e.,  by  observing  the 
direction  of  the  planet  from  the  earth,  and  at  the  same  time 
measuring  its  apparent  diameter  in  order  to  get  its  relative  dis- 
tances at  different  times.  Practically,  however,  the  method 
would  not  succeed  very  well,  since  the  planet's  apparent 
diameter  is  too  small  to  permit  the  necessary  precision  in  deter- 
mining the  variations  of  distance. 

A  motion  of  the  kind  represented  in  the  figure  is  loosely 
called  "  epicycloidal,"--not  quite  accurately,  because  the  orbits 
concerned  are  not  true  circles,  so  that  the  loops  are  of  varying 
size. 

The  Ptolemaic  theory  of  the  solar  system  was  fundamentally 
an  acceptance  of  this  apparent  motion  of  the  planets  relative  to 
the  earth  as  real,  though  his  theory  involved  certain  serious 
errors  of  arrangement  and  proportion. 

355.  Motion  of  a  Planet  on  the  Celestial  Sphere,  i.e.,  in  Right 
Ascension  and  Decimation,  or  in  Latitude  and  Longitude.  — Look- 
ing at  Fig.  127,  we  see  that,  viewed  from  the  earth,  the  planet 
moves  most  of  the  time  "  direct,"  i.e.,  eastward  in  the  direction 
of  the  arrow,  as  at  the  points  aa ;  but  while  rounding  the  loops 
at  bb,  where  it  comes  nearest  the  earth,  its  apparent  motion  is 
reversed  and  "  retrograde,"  and  at  certain  points,  cc,  on  each 
side  of  the  loop  the  planet  is  "  stationary  "  in  the  sky,  its 
motion  at  the  time  being  directly  towards  or  from  the  earth. 

Starting  from  the  time  of  superior  conjunction,  when  the 
planet  is  at  a,  it  moves  eastward,  or  "  direct,"  among  the  stars, 
always  increasing  its  right  ascension  or  longitude,  but  at  a  rate 
continually  slackening,  until  at  last  the  planet  becomes  "station- 
ary "  at  an  elongation  from  the  sun,  which  depends  upon  the 
size  of  the  orbit  and  its  distance  from  the  earth. 

From  the  stationary  point  it  reverses  its  course  and  moves 
westward  around  the  loop  until  it  comes  to  the  second  station- 
ary point  on  the  other  side  of  the  sun,  at  a  distance  the  same 
(for  a  circular  orbit)  as  that  of  the  former  stationary  point. 


THE   PLANETS   IN    GENERAL 


319 


There  it  resumes  its  eastward  motion  and  continues  it  until  it 
reaches  the  next  superior  conjunction,  at  the  end  of  a  synodic 
period. 

The  middle  of  this  arc  of  regression  is  always  very  near  the 
point  where  the  planet  comes  nearest  the  earth,  i.e.,  at  "  oppo-  pianet 
sition"  for  a  superior  planet,  and  at  "inferior  conjunction"  for  retr°grades 
an  inferior  planet.    In  time,  as  well  as  in  the  number  of  degrees  nearest 
passed  over,  the  direct  motion  always  exceeds  the  retrograde  in  the  eartn- 
each  synodic  period  of  the  planet. 

As  observed  with  a  transit-instrument,  all  planets  when 
moving  eastward  (direct)  come  later  to  the  meridian  each  night 
by  the  sidereal  clock,  and  vice  versa  when  retrograding. 

356.   Motions  in  Latitude.  —  If  the  orbits  of  the  planets  all  lay  Motion  in 
precisely  in  the  same  plane  with  the  earth's  orbit,  their  apparent  latitude: 


FIG.  128.  —  Motion  of  Saturn  and  Uranus  in  1897 

orbits  relative  to  the  earth  would  do  so  also,  and  their  apparent 
motions  on  the  celestial  sphere  would  be  simply  forward  and 
backward  upon  the  ecliptic. 

But  while  the  orbits  of  the  larger  planets  are  only  slightly 
inclined  to  the  ecliptic,  so  that  they  never  go  very  far  from  it, 
they  do,  in  fact,  deviate  a  few  degrees  one  side  and  the  other, 


320 


MANUAL   OF   ASTRONOMY 


so  that  their  paths  in  the  heavens  form  more  or  less  complicated 
loops  and  kinks.  Fig.  128  shows  the  loops  made  by  Saturn 
and  Uranus  in  1897,  when  they  happened  to  be  very  near  each 
other  in  the  sky. 

Certain  of  the  "  asteroids  "  have  orbits  greatly  inclined  to  the  ecliptic 
and  very  eccentric,  as,  for  instance,  the  little  Eros.  The  description  of 
apparent  motions  as  given  above  would  therefore  require  very  serious  modi- 
fication in  their  case.  Eros  is  sometimes  found  in  circumpolar  regions 
more  than  40°  north  of  the  ecliptic ;  sometimes  its  nearest  approach  to  the 
earth  does  not  coincide  with  the  time  of  its  opposition  within  several 
weeks;  and  sometimes  at  the  time  of  its  opposition  its  motion  is  more 
nearly  from  north  to  south  than  from  east  to  west. 

357.  Motion  of  the  Planets  in  Elongation,  i.e.,  with  Respect  to 
the  Sun's  Place  in  the  Sky.  —  The  visibility  of  a  planet  depends 
mainly  on  its  elongation,  because  when  near  the  sun  the  planet 
will  be  above  the  horizon  only  by  day.  As  regards  their  motion, 
considered  from  this  point  of  view,  there  is  a  marked  difference 
between  the  inferior  planets  and  the  superior. 

(1)  The  Superior  Planets  drop  always  steadily  westward  with 
respect  to  the  sun's  place  in  the  heavens,  continually  increasing 
their  western  elongation  or  decreasing  their  eastern.  As 
observed  by  an  ordinary  timepiece  (keeping  solar  time),  they 
therefore  invariably  rise  earlier  and  come  earlier  to  the  meridian 
every  successive  night,  never  moving  eastward  among  the  stars 
as  rapidly  as  the  sun,  even  when  their  direct  motion  is  most 
rapid.  This  relative  motion  westward  with  respect  to  the  sun 
is  not,  however,  uniform.  It  is  slowest  near  superior  conjunc- 
tion, most  rapid  at  opposition. 

Beginning  at  conjunction  the  planet  is  then  behind  the  sun, 
at  its  greatest  distance  from  the  earth,  and  invisible.  It  soon, 
however,  reappears  in  the  morning,  rising  before  the  sun  as  a 
"  morning  star,"  and  passes  on  to  western  quadrature,  when  it 
rises  at  midnight.  Thence  it  moves  on  to  opposition,  when  it 
is  nearest  and  brightest,  and  rises  at  sunset.  Still  dropping 


THE   PLANETS   IN   GENERAL  321 

westward  and  receding,  it  by  and  by  reaches  eastern  quadrature 
and  is  on  the  meridian  at  sunset.  Thence  it  still  crawls  slug- 
gishly westward  as  an  "evening  star,"  until  it  is  lost  in  the 
twilight  and  completes  its  synodic  period  by  again  reaching 
conjunction. 

358,  (2)  The  Inferior  Planets,  on  the  other  hand,  apparently  inferior 
oscillate  across  the  sun,   moving  out  equal,  or  nearly  equal,  Planets 

.        ,  '  oscillate 

distances    on    each    side    ot    it,    but    making    the    westward  from  one 
swing  between  us  and  the  sun  much  more  quickly  than  the  sideofsun 

,  to  the  other 

eastward. 

At  superior  conjunction  an  inferior  planet  is  moving  east- 
ward faster  than  the  sun.     Accordingly,  it  creeps  out  into  the 
twilight  as  an   "evening  star,"  and  continues  to  increase  its 
apparent  distance  from  the  sun  until  it  reaches  its  greatest  east- 
ern elongation  (47°  for  Venus  ;  for  Mercury,  from  18°  to  28°). 
Then  the  sun  begins  to  gain  upon  it,  and  as  the  planet  itself 
soon  begins  to  retrograde,  the  elongation  diminishes  rapidly  and  The  west- 
the  planet  hurries  back  to  inferior  conjunction,  passes  it,  and  ward  swmg 
then  as   a  "morning  star"   moves  swiftly  out  to  its  western  swifter 
elongation.     There  it  turns  and  climbs  slowlv  back  to  superior  than  the 

.         x.  J  eastward. 

conjunction  again. 

359.  The  Ptolemaic  System.  —  Assuming  the  fixity  and  cen-  The  system 
tral  position  of   the  earth    and   the   actual  revolution  of   the 
heavens,  Ptolemy  (who  flourished  at  Alexandria  about  A.D.  140)  ge5t. 
worked  out  the  system  which  bears  his  name. 

In  his  great  work,  the  Almagest  (Arabic  for  the  Greek  The 
G-reatest),  which  for  fourteen  centuries  was  the  authoritative 
"Scripture  of  astronomy,"  he  showed  that  all  the  apparent 
motions  of  the  planets,  so  far  as  then  observed,  could  be 
accounted  for  by  supposing  each  planet  to  move  around  the 
circumference  of  a  circle  called  the  "epicycle,"  while  the  center  The  epicycle, 
of  this  circle,  sometimes  called  the  "  fictitious  planet,"  itself  &ftiiious 

planet,  and 

moved  around  the  earth  on  the  circumference  01  another  and  deferent, 
larger  circle,  called  the  "  deferent." 


322 


MANUAL   OF   ASTRONOMY 


Error  of 
Ptolemy 
in  respect  to 
orbits  of 
Mercury 
and  Venus. 


Epicycles 
added  by  the 
Arabian 
astron- 
omers.   The 
Alphonsine 
tables. 


System  of 
Copernicus. 


It  was  as  if  the  real  planet  was  carried  on  the  end  of  a  crank 
arm  which  turned  around  the  "  fictitious  planet "  as  a  center  in 
such  a  way  as  to  point  towards  or  from  the  earth  at  times 
when  the  planet  is  in  line  with  the  sun. 

Fig.  129  represents  this  Ptolemaic  system,  except  that  no 
attention  is  paid  to  dimensions,  the  deferents  being  spaced  at 
equal  distances. 

It  will  be  noticed  that  the  epicycle  radii,  which  carry  at  their  extremi- 
ties the  planets  Mars,  Jupiter,  and  Saturn,  are  always  parallel  to  the  line 
which  joins  the  earth  and  the  sun. 

In  the  case  of  Venus  and  Mercury  this  was  not  so.  Ptolemy  supposed 
that  for  these  planets  the  deferent  circles  lay  between  the  earth  arid  the  sun, 
and  that  the  fictitious  planet  in  both  cases  revolved  in  its  deferent  once  a 
year,  always  keeping  exactly  between  the  earth  and  the  sun ;  the  motion 
in  the  epicycle  in  this  case  was  completed  in  the  time  of  the  planet's  period. 
He  did  not  recognize  that  for  these  two  planets  there  should  be  only  one 
deferent,  viz.,  the  orbit  of  the  sun  itself,  as  the  ancient  Egyptians  are  said 
to  have  understood. 

To  account  for  some  of  the  irregularities  of  the  planets'  motions  it  was 
necessary  to  suppose  that  both  the  deferent  and  epicycle,  though  circular, 
are  eccentric,  the  earth  not  being  exactly  in  the  center  of  the  deferent,  nor 
the  "  fictitious  planet  "  in  the  exact  center  of  the  epicycle.  In  after  times, 
when  the  knowledge  of  the  planetary  motions  had  become  more  accurate,  the 
Arabian  astronomers  added  epicycle  upon  epicycle  until  the  system  became 
very  complicated. 

King  Alphonso  of  Spain  is  said  to  have  remarked  to  the  astronomers 
who  presented  to  him  the  Alphonsine  tables  of  the  planetary  motions, 
which  had  been  computed  under  his  orders,  that  "  if  he  had  been  present 
at  the  creation  he  would  have  given  some  good  advice." 

360.   The    Copernican    System.  —  Copernicus     (1473-1543) 

asserted  the  diurnal  rotation  of  the  earth  on  its  axis,  which  was 
rejected  by  Ptolemy,  and  showed  that  it  would  fully  account 
for  the  apparent  diurnal  revolution  of  the  stars.  He  also 
showed  that  nearly  all  the  known  motions  of  the  planets  could 
be  accounted  for  by  supposing  them  to  revolve  around  the  sun, 
with  the  earth  as  one  of  them,  in  orbits  circular,  but  slightly 


THE   PLANETS   IN   GENERAL 


323 


out  of  center.  His  system,  as  he  left  it,  was  nearly  that  which 
is  accepted  to-day,  and  Fig.  125  may  be  taken  as  representing 
it.  He  was,  however,  obliged  to  retain  a  few  small  epicycles 
to  account  for  certain  of  the  irregularities. 

Up  to  this  time  no  one  dared  to  doubt  the  exact  circularity 
of  celestial  orbits.     It  was  considered  metaphysically  improper 
that  heavenly  bodies  should  move  in  any  but  perfect  curves,  Discovery 
and   the    circle   was   regarded   as    the    only   perfect   one.      It  of.th® 


form  of 
orbits  by 
Kepler. 


FIG.  120.  —The  Ptolemaic  System 

was  left  for  Kepler,  some  sixty  years  later  than  Copernicus, 
to  show  that  the  planetary  orbits  are  elliptical  and  to  bring 
the  system  substantially  into  the  form  in  which  we  know  it 
now. 

It  was  nearly  a  century  before  the  Copernican  system,  with 
the  improvements  of  Kepler,  finally  replaced  the  Ptolemaic. 
In  our  oldest  American  universities,  Harvard  and  Yale,  the 
Ptolemaic  was  for  a  considerable  time  taught  in  connection 
with  the  Copernican. 


324 


MANUAL   OF   ASTRONOMY 


System  of 
Tycho. 
He  could 
not  detect 
any  parallax 
of  the  stars 
and  con- 
cluded that 
the  earth 
must  be 
at  rest. 


361,  Tychonic  System.  — Tycho  Brahe,  who  came  between  Copernicus 
and  Kepler,  found  himself  unable  to  accept  the  Copernican  system  for  two 
reasons.     One  was  that  it  was  unfavorably  regarded  by  the  church,  and  he 
was  a  good  churchman.     The  other  was  the  really  scientific  objection  that 
if  the  earth  moved  around  the  sun,  the  fixed  stars  all  ought  to  appear  to 
move  in  a  corresponding  manner,  each  star  describing  annually  an  oval  in 
the  heavens  of  the  same  apparent  dimensions  as  the  earth's  orbit  seen  from 
the  star.     Technically  speaking,  they  ought  to  have  an  annual  parallax. 

His  instruments  were  by  far  the  most  accurate  that  had  ever  been  made, 
and  he  could  detect  no  such  parallax  (although  it  really  existed  and  can 
now  be  observed)  ;  hence,  he  concluded,  not  illogically,  but  incorrectly,  that 
the  earth  must  be  at  rest. 

He  rejected  the  Copernican  system,  placed  the  earth  at  the  center  of  the 
universe,  according  to  the  then  received  interpretation  of  Scripture,  made 
the  sun  revolve  around  the  earth  once  a  year,  and  then  (this  was  the  pecul- 
iarity of  his  system)  made  the  apparent  orbit  of  the  sun  the  common  defer- 
ent for  the  epicycles  of  all  the  planets,  making  them  to  revolve  around  the 
sun. 

This  theory  just  as  fully  accounts  for  all  the  motions  of  the  planets  as 
the  Copernican  or  Ptolemaic,  but  like  the  Ptolemaic  breaks  down  abso- 
lutely when  it  encounters  the  aberration  of  light  and  the  annual  parallax 
of  the  stars,  now  observable  with  modern  instruments,  though  not  with 
Tycho's.  The  Tychonic  system  was  never  generally  accepted,  and  the 
Copernican  was  soon  firmly  established  by  Kepler  and  Newton. 

362.  Elements  of  a  Planet's  Orbit.  —  These  are  a  set  of  numer- 
ical quantities,  seven  in  number,  which  describe  the  orbit  with 
precision  and  furnish  the  means  of  finding  the  planet's  place  in 
the  orbit  at  any  given  time,  whether  past  or  future,  so  far  as 
that  place  depends  upon  the  attraction  of  the  sun  alone.     They 
are  as  follows : 

(1)  The  semi-major  axis,  a. 

(2)  The  eccentricity,  e. 

(3)  The  inclination  to  the  ecliptic,  i. 

(4)  The  longitude  of  the  ascending  node,  Q>. 

(5)  The  longitude  of  perihelion,  TT. 

(6)  The  period,  P,  or  else  the  daily  motion,  p. 

(7)  The  epoch,  E. 


THE   PLANETS   IN   GENERAL 


325 


Of  these,  the  first  five  pertain  to  the  orbit  itself,  regarded  as 
an  ellipse  lying  in  space  with  one  focus  at  the  sun,  while  two 
are  necessary  to  determine  the  planet's  place  in  the  orbit. 

363.    The  semi-major  axis,  a  (CA  in  Fig.  130),  defines  the  Size  defined 
size  of  the  orbit  and  is  usually  expressed  in  astronomical  units.     y  * 
(It  will  be  remembered  that  the  earth's  mean  distance  from  the 
sun  is  the  "  astronomical  unit.") 

The  eccentricity,  e,  defines    the  orbit's  form.     It  is  a  mere  Form 

Q  defined 

numerical  quantity,  being  the  fraction  -->  obtained  by  dividing  by  the 

a  eccentricity, 

the  distance  between  the  sun  and  the  center  of  the  orbit  by  the 


FIG.  130.  —  The  Elements  of  a  Planet's  Orbit 

semi-major  axis.  In  some  computations  it  is  convenient  to  use, 
instead  of  the  decimal  fraction  itself,  the  angle  c£,  which  has  e 
for  its  sine,  so  that  e  =  sin  <£. 

The  third  element,  i,  the  inclination,  is  the  angle  between  the  inclination 
plane  of  the  planet's  orbit  and  that  of  the  earth.     In  the  figure  and  longi~ 
it  is  the  angle  KNO,  the  plane  of  the  ecliptic  being  lettered  determine 
EKLP  and  that  of  the  orbit   ORB  T.  plane  of 

The  fourth  element,  Q  (the  longitude  of  the  ascending  node), 
defines  what  has  been  called  the  "aspect"  of  the  orbit  plane, 
i.e.,  the  direction  in  which  it  faces.  The  line  of  nodes  is  the  line 


326 


MANUAL   OF   ASTRONOMY 


The  period 
and  epoch 
furnish  the 
means  of 
computing 
the  place  of 
planet  in 
its  orbit. 


NNr  in  the  figure  (the  intersection  of  the  two  planes  of  the 
orbit  and  ecliptic),  and  the  angle  °p  SN  is  the  longitude  of  the 
ascending  node.  The  planet  passes  from  the  lower  or  southern 
side  of  the  plane  of  the  ecliptic  to  the  northern  at  the  point  n 
in  its  orbit. 

The  fifth,  and  last,  of  the  elements  which  belong  strictly  to 
the  orbit  itself  is  TT,  the  so-called  longitude  of  the  perihelion, 
which  defines  the  direction  in  which  the  major  axis  of  the  ellipse 
(the  line  pA)  lies  on  the  plane  ORBT.  Strictly,  TT  is  not  a 
longitude,  but  equals  the  sum  of  the  two  angles  &  and  o> ;  i.e., 
°f  SN  (in  the  plane  of  the  ecliptic)  plus  NSp  (in  the  plane  of 
the  orbit),  both  reckoned  in  the  direction  of  the  planet's  motion. 
NSp,  or  co,  in  the  figure  is  about  210°  and  °f  Sp  is  about  315°. 

If  we  regard  the  orbit  as  an  oval  wire  hoop  suspended  in 
space,  these  five  elements  completely  define  its  position,  form, 
and  size.  The  plane  of  the  orbit  is  fixed  by  the  two  elements 
numbered  three  and  four,  the  position  of  the  orbit  in  this  plane 
by  number  five,  the  form  of  the  orbit  by  number  two,  and  finally 
its  magnitude  by  number  one. 

To  determine  where  the  planet  will  be  at  any  subsequent 
date  we  need  two  more  elements  : 

Sixth,  the  periodic  time.  We  must  have  the  sidereal  period, 
P,  or  else  the  mean  daily  motion,  /u,  which  is  simply  360°  divided 
by  the  number  of  days  in  P. 

Seventh,  and  finally,  we  must  have  a  "starting-point,"  the 
Epoch,  so  called;  i.e.,  the  longitude  of  the  planet  as  seen 
from  the  sun  at  some  given  date,  usually  Jan.  1,  1850  or  1901, 
or  else  the  precise  date  at  which  the  planet  passed  the  perihelion 
or  the  node. 

364.  If  no  force  acted  on  the  planets  except  the  sun's  attrac- 
tion, these  elements  would  never  change,  but  on  account  of  the 
interaction  of  the  planets  they  do  change ;  accordingly,  it  is 
usual  to  add  in  tables  of  the  elements  columns  giving  the 
amount  by  which  each  element  changes  in  a  century. 


THE  PLANETS  IN  GENERAL  327 

It  is  to  be  noted  also  that  if  Kepler's  third  law  in  its  uncor- 
rected  form  were  strictly  true,  as  it  is  not  (Sec.  308),  we  should 
not  need  both  a  and  P,  for  if  a  is  expressed  in  astronomical 
units,  P  in  years  would  be  simply  V#3. 

The  method  of  determining  the  position  of  a  planet  in  its  orbit,  i.e.,  of 
computing  an  ephemeris,  belongs  to  theoretical  astronomy  and  will  not  be 
treated  here.  It  is  sufficient  to  say  that  it  is  possible  from  the  elements 
of  the  planets  to  deduce,  for  any  given  time,  their  actual  positions  in  their 
orbits  and  their  distances  and  directions  from  the  sun  and  from  each 
other. 

DETERMINATION   OF  THE  PERIOD  AND  DISTANCE  OF 

A  PLANET 

365.  Since  the  planetary  orbits  are,  for  the  most  part,  nearly 
circular  and  in  the  plane  of  the  ecliptic,  they  are  described  with 
sufficient  accuracy  for  ordinary  purposes  by  simply  giving  the 
planet's  period  and    distance    from  the    sun.     We  proceed  to 
show  how  these  two  elements  may  be  determined,  but  note  in  General 
passing  that  there  is  a  qeneral  method  by  which  all  seven  of  the  method  of 

J  Gauss  for 

elements  of  a  planet's  orbit  can  ordinarily  be  deduced  together  computing 
from  three  accurate  observations  of  the  planet's  position,  sepa-  a11  the  ele~ 
rated  by  a  few  weeks'  interval,  though  in  certain  special  cases  pianet  from 

&  fourth  observation  becomes  necessary.  three  com- 

plete obser- 

This  general  method  involves  long  and  complicated  calculation, — treated   vations. 
in  works  on  theoretical  astronomy.     It  was  invented  in  1801  by  Gauss, 
then  a  young  man  of  twenty-three,  in  connection  with  the  discovery  of 
Ceres,  the  first  of  the  asteroids,  which,  after  its  discovery  by  Piazzi,  was 
lost  to  observation  by  passing  into  conjunction  with  the  sun. 

366.  The  observations  upon  which  the   calculation  for  the 
elements   of   a   planet's   orbit  rest  are   determinations   of  the 
planet's  right  ascension  and  declination,  usually  made   with 
the  meridian-circle,  but  sometimes  by  the  differential  method 
(Sees.  116-117)  with  the  equatorial  telescope  and  micrometer, 
or  often  at  present  by  photography. 


328  MANUAL    OF   ASTRONOMY 

These  observations  are,  of  course,  made  from  the  earth's  sur- 
face, and  before  they  can  be  utilized  must  be  corrected  for  paral- 
lax, so  as  to  give  the  geocentric  place,  i.e.,  the  place  the  planet 
would  occupy  if  seen  from  the  center  of  the  earth.     In  many 
cases  the  geocentric  right  ascension  and  declination  must,  for 
convenient  use,  be  further  transformed  into  celestial  latitude 
and  longitude.     (See  Sec.  30  arid  Appendix,  Sec.  702.) 
interpoia-          367.   Interpolation  of  Observations.  —  It  often  happens  that 
tion  of  we  want  the  place  of  a  planet  at  some  particular  moment  when 

observations 

to  furnish  a  it  cannot  be  actually  observed,  as,  for  instance,  when  it  is  below 
planet's  ^ne  horizon.  If  we  have  a  series  of  observations  made  about 
moment  that  time,  say  for  several  days  before  and  after,  the  place  at 
when  it  any  moment  included  within  the  time  covered  by  the  observa- 
actuaiiv  tions  can  be  determined  by  interpolation,  and  with  an  accuracy 
observed.  exceeding  that  of  any  single  observation  of  the  series. 

The  determination  can  be  made  graphically  by  simply  plot- 
ting the  observations  on  squared  paper  with  a  scale  of  times  as 
abscissas,  the  observed  data  being  plotted  as  ordinates,  and  then 
drawing  a  curve  through  the  points  determined  by  observation, 
as  in  so  many  operations  of  the  physical  laboratory.  Whatever 
can  be  done  graphically  can,  of  course,  be  worked  out  still  more 
accurately  by  calculation.  The  principle  is  of  very  extensive 
application. 

Heliocentric       368.    Heliocentric  Place.  —  This  is  the  place  of  a  planet  as  it 

place.  would  be  seen  from  the  sun  and  is  often  wanted  in  calculations. 

When  we  have  once  found  the  node  of  the  planet's  orbit  and 

the  inclination  of  the  orbit,  as  well  as  the  planet's  distance  from 

the  sun,  the  heliocentric  place  and  the  distance  of  the  planet 

from  the  earth  can  be  immediately  deduced  from  the  geocentric 

by  a  simple  calculation,  which,  though  not  difficult,  is  rather 

tedious  and  lies  outside  the  scope  of  this  work.     (See  Watson's 

Theoretical  Astronomy,  p.  86.) 

369.  Determination  of  the  Sidereal  Period  of  a  Planet.  —  First, 
by  Observation  of  its  Node  Passage.  At  the  moment  when  a 


THE  PLANETS  IN  GENERAL  329 

planet  crosses  its  node  its  latitude,  both  geocentric  and  heliocen-  Determina- 
tric,  becomes  zero,  because  the  planet  is  then  actually  in  the  tionof>a 
plane  of  the  ecliptic.     From  a  series  of  observations  of  its  right  period  by 
ascension  and  declination  made  about  that  time  and  reduced  to  observa- 
latitude  and  longitude,  both  the  position  of  the  node  and  the  When  it 
time  when  the  planet  crossed  the  node  can  be  deduced.  passes  the 

The  interval  between  two  successive  node  passages  thus 
determined  is  the  planet's  period,  —  exactly,  if  the  node  be  sta- 
tionary; very  approximately  in  any  case,  for  none  of  the  nodes 
move  rapidly. 

The  method  is  not  very  satisfactory,  however,  (1)  because  the 
planetary  orbits  cross  the  ecliptic  at  so  small  an  angle  that  the 
latitude  is  almost  zero  for  many  hours,  so  that  the  precise  sec- 
ond is  difficult  to  determine ;  (2)  then,  also,  the  periods  of  the 
more  distant  planets  are  too  long,  —  Uranus,  84  years ;  Neptune, 
164  years,  —  too  long  to  wait. 

370.    Second,    by  the    Mean   Synodic    Period.     The    sidereal  Period 
period  may  also  be   determined  bv  finding   the   mean  synodic  determmed 

fromobser- 

period  of  a  planet  trom  the  dates  01  two  conjunctions  or  oppo-  rations  of 
sitions,  widely  separated  in  time  if  possible.  time  of  con- 

™  .  „  •      p  -i    p  f      •    ^  ,    junction  or 

The  exact  instant  of  syzygy  is  found  irom  a  series  or  right  opposition, 
ascensions  and  declinations  observed  about  the  proper  date ;  by 
comparing  the  deduced  longitudes  of  the  planet  with  the  corre- 
sponding longitudes  of  the  sun  we  find  easily  the  precise  moment 
when  the  difference  was  0°  or  180°.  When  the  synodic  period  is 
found  the  sidereal  is  at  once  given  by  the  equations  in  Sec.  351, 

111  ,111, 

viz.,  —  = ior  an  interior  planet,  and  —  = tor  a 

Cf    vx      77f  Cf  }/     ~jjl 

superior.     In  the  first  case,  P  =  —     -;  in  the  second,  P  =  —     —• 

S  +  1S  S  —  E     Necessary 

It  will  not  answer  for  this  purpose  to  deduce  the  synodic  oppositions 
period  from  two  successive  oppositions,  because,  on  account  of  should  be 
the  eccentricity  of  the  orbits,  both  of  the  planet  and  of  the  earth,  ^iTiong 
the  synodic  periods  are  notably  variable.     The  observations  must  interval. 


330 


MANUAL   OF   ASTRONOMY 


Geometrical 
method  of 
determining 
a  planet's 
distance 
from  the 
sun  by  two 
observa- 
tions of  its 
elongation 


by  an 

interval 

of  time 

exactly 

equal  to  the 

planet's 

period. 


be  sufficiently  separated  in  time  to  give  a  good  determination 
of  the  mean  synodic  period. 

In  the  case  of  all  the  older  planets  we  have  observations  run- 
ning back  nearly  two  thousand  years,  so  that  no  difficulty  arises 
on  this  score.  For  the  newly  discovered  planets  the  method 
would  ,be  seldom  available. 

371,  Geometrical  Method  of  determining  a  Planet's  Distance 
from  the  Sun  in  Astronomical  Units.  —  When  we  know  a  planet's 
sidereal  period  it  is  easy  to  determine  its  distance  from  the  sun 
by  two  observations  of  the  planet's  elongation  from  the  sun,  made 
at  dates  separated  by  an  interval  of  exactly  one  of  its  periods. 

The  elongation,  it  will  be  remembered,  is  the  difference 
between  the  longitude  of  the  planet  and  that  of  the  sun  as  seen 
from  the  earth,  and  is  determined  for  any  given  date  by  a  series 
of  meridian-circle  observations  of  the  planet  and  sun  covering 
that  date. 

To  determine,  for  instance,  the  distance  of  Mars  we  must 
have  two  observations  of  the  planet's  elongation,  MAS  and  MCS 
(Fig.  131),  separated  by  an  interval  of  686.95  days;  so  that  at 
the  moment  of  the  second  observation  from  the  earth  at  C  the 
planet  will  occupy  precisely  the  same  point  in  its  orbit  as  when 
observed  from  A  nearly  two  years  before. 

In  the  figure  the  two  angles  at  A  and  C  are  given  directly 
by  the  observations.  The  angle  at  the  sun,  ASC,  is  determined 
from  the  earth's  motion  during  the  elapsed  time,  which  is  less  than 
two  sidereal  years  by  730.53  days  minus  686.95  days,  i.e.,  by 
43.58  days;  this  makes  the  angle  ASC  very  nearly  43°. 

The  sides  AS  and  CS  are  radii  vectores  of  the  earth's  orbit, 
accurately  known  in  terms  of  the  mean  distance  of  the  earth 
from  the  sun,  which  is  the  astronomical  unit. 

In  the  quadrilateral  SAMC  we  have,  therefore,  the  three 
angles  A,  S,  and  C  given,  and  the  two  sides  AS  and  CS;  we 
can,  therefore,  proceed  just  as  in  Sec.  196  in  computing  the 
line  SM,  finding  both  its  length  as  compared  with  AS,  the 


THE   PLANETS   IN   GENERAL 


331 


astronomical  unit,  and  also  the  planet's  direction  from  the  sun, 
given  by  the  angle  ASM  or  CSM,  both  of  which  come  out  in  the 
course  of  the  calculation. 

The  student  can  follow  out  for  himself  the  process  by  which  from  two 
elongations  of  Venus,  SAV&nd  SBV,  observed  at  an  interval  of  225  day  a, 
SV  can  be  determined.  A  little  modification  is  necessary  from  the  fact 


FIG.  131.  —  Determination  of  the  Distance  of  a  Planet  from  the  Sun 

that  the  point  S  falls  within  the  triangle  formed  by  the  two  positions  of 
the  earth  and  planet,  instead  of  outside  of  it,  as  in  the  case  of  Mars. 

372.  From  a  sufficient  number  of  such  pairs  of  observations 
distributed  around  an  orbit  it  is  evidently  possible  to  work  out 
completely  its  magnitude  and  form ;  and  it  was  precisely  in 
this  way  that  Kepler,  utilizing  the  rich  mine  of  data  contained 
in  Tycho's  long  series  of  observations,  proved  that  the  orbit  of 
Mars  is  an  ellipse  (and  later  those  of  the  other  planets  also)  and 


This  method 
used  by 
Kepler  in 
proving  the 
orbit  of 
Mars  to  be 
an  ellipse. 


332 


MANUAL   OF   ASTRONOMY 


The  distance 
of  an 
inferior 
planet  deter- 
mined by  a 
single  obser- 
vation of  its 
greatest 
elongation. 


Planetary 
perturba- 
tions : 
periodic 
and  secular. 


deduced  their  distances  from  the  sun  as  compared  with  that  of 
the  earth.  His  Harmonic  Law  was  then  discovered  by  simply 
comparing  the  periods  with  the  distances.  Now  that  we  have 
the  Harmonic  Law,  a  planet's  approximate  mean  distance  can, 
of  course,  after  its  period  is  known,  be  much  more  easily  found 
by  applying  that  law  than  by  the  geometrical  method  just 
explained. 

373.  Simple  Method  of  finding  the  Distance  of  an  Inferior 
Planet. —  In  the  case  of  Venus,  which  has  an  orbit  almost  per- 
fectly circular,  we  can  use  the 
method  indicated  in  Fig.  132. 
When  the  planet  is  at  its  great- 
est elongation  the  angle  at  V 
is  sensibly  a  right  angle,  and 
if  we  then  measure  the  elonga- 
tion SEV,  we  have  at  once  SV 
=  SJEX  sin  SEV. 

Mercury's  orbit  is  so  eccen- 
tric that  the  method  gives  only  a 
rough  approximation,  the  angle 
at  M  not  being  a  right  angle ; 

but,  by  taking  many  observations  distributed  all  around  the 

orbit,  an  accurate  result  may  be  obtained. 

374.  Planetary  Perturbations.  —  The  attractions  of  the  planets 
for  each  other  slightly  disturb  their  otherwise  elliptical  motion 
around  the  sun,  but  their  disturbing  forces  are,  with  few  excep- 
tions, extremely  small,  and  the  resulting  perturbations  are,  as  a 
rule,  much  less  than  in  the  case  of  the  moon.    The  exception  is  in 
the  case  of  some  of  the  asteroids,  which  at  times  come  near  enough 
to  the  gigantic  Jupiter  to  be  displaced  by  as  much  as  8°  or  10°. 
The  interaction  between  Jupiter  and  Saturn  also  produces  appar- 
ent displacements  of  these  planets  exceeding  half  a  degree. 

The  planetary  perturbations   are   divided  into  two  classes: 
(1)  the  periodic  perturbations,  which  depend  on  the  positions 


FIG.  132.  —  Distance  of  an  Inferior  Planet 
determined  by  Observations  of  its 
Greatest  Elongation 


THE   PLANETS   IN   GENERAL  333 

of  the  planets  in  their  orbits  and  affect  their  orbital  positions 
(these  generally  run  through  their  cycle  within  a  century) ; 
(2)  the  secular  perturbations,  which  depend  on  the  relative  posi- 
tions of  the  orbits  themselves  with  reference  to  each  other  and 
produce  changes  in  the  elements  of  the  orbits  affecting  the  positions 
of  the  planets  only  indirectly  (these  have  periods  of  thousands, 
and  even  millions,  of  years). 

375.  Periodic  Perturbations.  —  Those  of  Mercury  never  exceed  Amount  of 
15",  as  seen  from  the  sun.     Those  of  Venus  may  reach  30" ;  the  Pe'iodic 

perturha- 

those  of  the  earth  about  1'  (say  30000  miles),  and  those  of  Mars  tionsof  the 
a  little  exceed  2'.     As  already  mentioned,  the  mutual  disturb-  dlfferent 

planets. 

ances  of  Jupiter  and  Saturn  are  much  larger,  reaching  28'  and 
48',  respectively.  Those  of  Uranus  never  reach  3',  as  seen  from 
the  sun,  and  those  of  Neptune  are  smaller  yet. 

The  great  perturbation  between  Jupiter  and  Saturn  is  called  a  "long 
inequality,"  having  a  period  of  913  years.  It  is  due  to  the  near  commen- 
surability  of  their  periods,  seventy-seven  of  Jupiter's  periods  being  almost 
exactly  equal  to  thirty-one  of  Saturn's.  Between  Uranus  and  Neptune 
there  is  a  somewhat  similar  "long  inequality"  with  a  period  exceeding 
4000  years. 

376.  Secular  Perturbations.  —  These,  as  already  said,  depend  Secular  per- 
upon  the  relative  positions  of  the  orbits,  but  not  of  the  planets  turbatlons 
themselves,  and  their  effects  are  to  change, the  orbits  and  only  orbits, 
indirectly  to  alter  the  positions  occupied  by  the  planets.     These 

secular  perturbations  are  extremely  slow  in  their  development, 
running  on,  as  the  name  implies,  "from  age  to  age." 

A    most    remarkable    fact,    first    proved    by   Laplace    and 
Lagrange   about  a  century  ago,  is   that  the    major   axes   and  Constancy 
periods  are   never  altered   by  these   "secular   perturbations." 
While  subject  to  slight  periodical  changes,  they  remain  abso-  periods, 
lutely  constant  in  the  long  run,  so  far  as  planetary  action  goes. 

The  nodes  and  perihelia,  on  the  other  hand,  move  around  Revolution 
continuously;  all  the  nodes  regress,  and  all  the  perihelia  (that  of^odes 
of  Venus  alone  excepted)  advance. 


334 


MANUAL   OF   ASTRONOMY 


According  to  Leverrier,  the  shortest  of  these  periods  of  revo- 
lution is  37000  years  (the  line  of  nodes  of  Uranus),  and  the 
longest  is  540000  (that  of  the  perihelion  of  Neptune).  But  these 
numbers  must  not  be  accepted  too  confidently,  since  the  rate  of 
motion  is  not  constant,  but  itself  is  subject  to  secular  variation. 

The  inclinations  of  the  orbits  to  the  ecliptic  are  all  slightly 
changed  in  an  irregular  oscillatory  manner,  some  increasing  and 
some  diminishing.  As  Laplace  and  Leverrier  have  proved, 
all  these  changes  are  for  the  principal  planets  confined  within 
narrow  limits  of  not  more  than  a  degree  or  two. 

The  eccentricities  also  change  in  the  same  irregular  way,  some 
increasing,  some  decreasing,  but  never  changing  greatly.  These 
oscillations,  both  for  inclinations  and  eccentricities,  usually 
occupy  from  10000  to  50000  years,  but  change  continually; 
a  long  and  extensive  swing  in  one  direction  may  or  may  not  be 
followed  by  a  short  one  reversing  its  effects. 

The  statements  made  with  reference  to  the  unimportant  character  of 
the  planetary  perturbations  do  not  apply  in  the  case  of  the  asteroids,  the 
orbits  of  which  may  possibly  be  subject  to  very  material  alterations. 

377.  Stability  of  the  Planetary  System.  —  About  a  hundred 
years  ago  Lagrange  and  Laplace  were  supposed  to  have  proved 
that  in  the  case  of  all  the  planets  (asteroids  excepted)  their 
mutual  attractions  could  never  subvert  the  system ;  that  the 
periods  and  major  axes  of  the  orbits  would  forever  remain  con- 
stant, while  the  inclinations  and  eccentricities  would  oscillate 
only  within  narrow  limits. 

Until  very  recently  their  conclusion  was  considered  irrefu- 
table ;  but  within  the  past  few  years  Poincare  has  shown  that 
the  infinite  series,  upon  the  summation  of  which  they  depended, 
instead  of  being  essentially  convergent,  as  they  supposed,  may 
become  divergent  when  millions  of  years  are  taken  into  account, 
and  that  therefore  their  conclusions  are  unsound.  If  so,  it  is  not 
impossible,  though  hardly  probable,  that  ultimately  the  mutual 


THE  PLANETS   IN   GENERAL  335 

attractions  of  the  planets  may  completely  change  their  orbits,  othercauses 
Other  conceivable  causes  also  might  bring  about  the  destruction  ^^it 
of  the  system;  such,  for  instance,  as  the  action  of  a  resisting 
medium  or  the  invasion  of  some  huge  body  from  outer  space. 

378.    The  "  Invariable  Plane."  —  There  is  no  reason  why  the  Theinvari- 
ecliptic— the  plane  of  the  earth's  orbit  — should  be  made  the  J^n^ne 
fundamental  plane  of   reference  for   the  solar  system,  except 
that  we  terrestrials  live  on  the  earth.     There  is  in  the  system, 
however,  an  "invariable  plane,"  as  discovered  by  Laplace  in 
1784,  the  position  of  which  remains  forever  unchanged  by  any 
mutual  action  between  the  bodies  of  the  system,  just  as  does 
their  common  center  of  gravity. 

This  plane  is  denned  by  the  following  conditions:  if  from  all  the 
planets  perpendiculars  are  drawn  to  it  (technically,  if  the  planets  be 
"  projected  "  on  this  plane,  which  passes  through  the  center  of  gravity  of  the 
system),  and  if  then  we  multiply  the  mass  of  each  planet  by  the  area  which 
its  projected  radius  vector  describes  upon  this  plane,  in  a  unit  of  time, 
around  the  center  of  gravity,  the  sum  of  the  products  will  be  a  maximum. 

The  determination  of  the  exact  position  of  this  plane  demands,  however,    Position  of 
an  accurate  knowledge  of  the  masses  and  motions  of  all  the  planets,  dis-  ^e  invari- 
covered  and  undiscovered,  belonging  to  the  system,  and  the  data  now  in   a    e  p  ane' 
our  possession  hardly  warrant  a  final  assignment  of  its  location.     Accord- 
ing to  the  most  recent  computation  (by  See),  it  is  inclined  to  the  present 
ecliptic  at  an  angle  of  1°  35"  07".75,  its  ascending  node  on  the  ecliptic  being 
in  longitude  106°  08'  46".5.     As  might  be  expected,  it  lies  between  the 
planes  of  the  orbits  of  Jupiter  and  Saturn,  and  very  near  to  that  of  Jupiter. 

THE   PLANETS   THEMSELVES 

In  discussing  the  "  personal  peculiarities  "  of  the  planets  we 
have  to  consider  a  variety  of  different  data,  mostly  obtained 
by  telescopic  study  and  micrometric  measurements,  —  such,  for 
instance,  as  their  diameters;  their  masses  and  densities;  their 
axial  rotation;  their  surface  markings;  their  atmospheric  phe- 
nomena, if  any;  their  albedo,  or  light-reflecting  power;  and, 
finally,  their  satellite  systems. 


336 


MANUAL   OF   ASTRONOMY 


Determina- 
tion of  a 
planet's 
diameter  by 
micrometric 
observa- 
tions. 


379.  Determination  of  "Size,"  —  Diameter,  Surface,  and 
Volume.  —  The  size  of  a  planet  is  found  by  measuring  its  appar- 
ent diameter  in  seconds  of  arc  with  some  form  of  "  micrometer  " 
(Sec.  71)  attached  to  a  powerful  telescope.  Since  from  the  ele- 
ments of  the  orbit  of  a  planet  and  of  the  earth  we  can  find  the 
distance  of  the  planet  from  the  earth  at  any  time  in  astro- 
nomical units,  we  can  at  once  deduce  the  real  linear  diameter 
from  the  apparent  diameter  D"  by  an  equation  slightly  modi- 
fied from  that  given  in  Sec.  10,  viz., 

linear  diameter  =  A  sin  D",  or 


The  planet's 
relative 
radius,  p. 


Surface  area 
equals  p2, 
volume 
equals  p3. 


Greater 
effect  of 
observa- 
tional error 
in  case  of 
remote 
planets. 


Planet's 
mass  deter- 
mined by 
means  of 
satellite. 


A  being  the  distance  of  the  planet  from  the  earth.  This  will 
give  the  linear  diameter  as  a  fraction  of  the  astronomical  unit 
and  can  be  converted  into  miles  by  simply  multiplying  it  by 
93  000000,  the  number  of  miles  in  the  unit. 

For  many  purposes  it  is  convenient  to  express  the  planet's 
radius  in  terms  of  the  earth's  radius  by  dividing  half  the  diame- 
ter in  miles  by  3959  (the  number  of  miles  in  the  mean  radius 
of  the  earth),  designating  this  relative  radius  by  p. 

The  surface  area  of  the  planet  in  terms  of  the  earth's  surface 
is  then  />2,  and  the  volume  or  bulk  of  the  planet  is  /o3  in  terms  of 
the  earth's  volume  ;  i.e.9  if,  as  is  nearly  true  in  the  case  of 
Jupiter,  p  =  11,  then  the  surface  of  the  planet  is  121  times  that 
of  the  earth,  and  its  bulk  1331  times  that  of  the  earth. 

The  nearer  the  planet,  other  things  being  equal,  the  more 
accurately  p  and  the  quantities  derived  from  it  can  be  deter- 
mined. An  error  of  O'M  in  measuring  the  apparent  diameter 
of  Venus  when  nearest  counts  for  less  than  thirteen  miles,  but 
in  the  case  of  Neptune  it  would  correspond  to  more  than  1300. 

380.  Mass,  Density,  and  Surface  Gravity.  —  If  the  planet  has 
a  satellite,  its  mass  compared  with  the  sun  is  very  easily  and 
accurately  found  from  the  proportion 


— 


THE   PLANETS   IN   GENERAL  337 

in  which  S  is  the  mass  of  the  sun,  p  that  of  the  planet,  A  the 
mean  distance  of  the  planet  from  the  sun,  and  T  the  planet's 
sidereal  period  ;  while  s  is  the  mass  of  the  satellite,  a  its  mean 
distance  from  the  planet,  and  t  its  sidereal  period. 

In  almost  all  cases  p  in  the  first  term  may  be  neglected  as 
Gompared  with  $,  and  in  the  second  term  s  as  compared  with  p, 
which  makes  the  proportion  read 

A*     a3  a3      T2 

S:P::Jv:p>   whence,   p  =  S  x  -  X  -^ 

If  we  want  the  mass  as  compared  with  the  earth,  the  first  Mass  of 
proportion  becomes  planet  com- 

pared  with 

(earth  +  moon)  :  (planet  -f  satellite)  the  earth. 

(cube  of  moon's  distance        \ 
square  of  moon's  sidereal  period/ 
f  /cube  of  satellite's  distance \ 
\square  of  satellite's  period/ ' 

The  mass  of  the  moon  being  ^  of  that  of  the  earth,  it  cannot 
be  neglected  in  comparison  with  the  earth's  mass.  (No  other 
satellite  has  a  mass  more  than  ^-Q-^  of  its  planet.) 

It  is  to  be  noted  also  that  instead  of  the  actual  sidereal  period 
of  the  moon  we  must  use  a  period  about  an  hour  shorter,  in 
order  to  allow  for  the  action  of  the  sun  (Sec.  327,  (1)). 

The  observations  upon  which  this  method  of  determining  a  Data  for 
planet's  mass  depend  are  those  of  the  satellite's  greatest  elonqa-  mass:  the 

y  y        satellite's 

tion,  the  measures  of  distance  being  especially  important,  since  distance  and 
the  distance  enters  into  the  formula  by  its  cube.  period. 

When  a  planet  has  no  satellite,  as  is  the  case  with  Mercury  Mass  of 
and  Venus,  its  mass  can  be  determined  only  by  means  of  the  Planet 

J       J  determined 

perturbations  it  produces  in  the  motions  of  other  planets,  or  of  by  the  per- 
comets  that  happen  to  come  near  it.  turbations 

.  it  causes. 

In  the  case  of  Mercury  the  mass  is  still  very  uncertain. 
Venus,  however,  disturbs  the  earth  sufficiently  to  give  a  very 
good  determination  of  her  mass. 


388 


MANUAL   OF  ASTRONOMY 


Demonstra-        381.   The  proportions  given  in  the  preceding  section  are  easily 
tionofthe      (jerive(i  for  circular  orbits  from  the  equation  for  the  general 

formula  for 

planet's         equation  of  the  motion  of  a  small  body  revolving  around  a  larger, 

mass.  v\rr 

VIZ.,  A       n  o 

,,_    .          ,          4-7T2        T-3  ._,. 

(M  +  m)  =  — -X-.  (1) 

v  G       t2 

This  equation  is  obtained  by  combining  the  equation  for  the 
gravitational  attraction  between  two  spheres  expressed  as  an 
acceleration  (Sec.  146),  viz., 


with  the  expression  for  the  central  force  in  circular  motion 
(Sec.  306),  viz.,  4  ^ 


Replacing  D  in  the  first  equation  by  r,  and  equating  the  two 
values  of  /,  we  have    ^M+m  r 

from  which  equation  (1)  follows  at  once. 

In  forming  the  proportion  the  constant  factor  drops  out,  and 


we  have 


M1  H- 


11..  la., 


As  Newton  proved,  this  is  accurately  true  for  elliptical  orbits 
also  if  for  r  we  put  a,  the  semi-major  axis  of  the  orbit;  but 
the  demonstration  lies  beyond  our  scope. 

382.  Surface  Gravity  and  Density.  —  When  the  mass  has  been 
determined  the  surface  gravity  and  density  follow  at  once. 
Putting  7  for  surface  gravity  as  compared  with  the  earth,  we 
have  m 

7  =  -r> 
P2 

m  being  the  planet's  mass,  and  p  its  radius  as  compared  with 
the  earth's.     The  density,  compared  with  the  earth,  is  simply 

fyy\ 

—  ;  if  we  want  the  specific  gravity,  i.e.,  density  as  compared  with 


THE   PLANETS  IN   GENERAL  889 

water,  we  must  multiply  the  result  by  5.53,  the  density  of  the 
earth.  Any  error  in  the  measured  diameter  of  course  affects 
very  seriously  the  computed  density  and  gravity. 

383.   Rotation  Period  and  Data  connected  with  it.  —  The  length  notation 
of  the  planet's  "  day,"  when  it  can  be  determined  at  all,  is  usually  I 
ascertained  by  observing  some  well-marked  spot  on  its  disk  and  planet's 
noting  the  times  of  its'  successive  returns.     An  approximate  e(iuator 

determined 

value  of  the  rotation  period  is  obtained  from  the  observation  of  by  observa- 
such  returns  during  a  few  days  or  weeks,  and  this  is  afterwards  tion  of  8P°ts 
corrected  by  data  furnished  from  observations  separated  by  the  Surface. 
longest  interval  obtainable, — a  century  or  more  if  possible. 

Mars,  however,  is  the  only  planet  of  which  the  rotation  period 
is  known  with  great  accuracy ;  the  others  either  show  no  well- 
defined  markings,  or  only  such  markings  as  seem  to  be  more  or 
less  movable  on  the  planet's  surface,  like  spots  on  the  sun. 

In  reducing  the  observations  account  has  to  be  taken  of  the 
continual  change  in  the  direction  of  the  planet  from  the  earth 
and  also  of  the  variations  of  its  distance,  which  alter  the  time 
taken  by  light  to  reach  us. 

In  the  case  of  the  little  planet  Eros,  a  large  and  regular  vari-  notation 
ation  in  its  brightness,  observed  for  some  months  early  in  1901   Penod  of 

5  .  t  Eros  deter- 

in  a  certain  portion  of  its  orbit,  was  probably  due  to  its  axial  mined  from 

rotation ;  if  so,  the  photometrically  measured  period  of  variation  variations 
of  brightness  gives  a  determination  of  the  length  of  its  day.  brightness. 
(See  Sec.  428.)     The  planet  is  far  too  small  to  show  a  disk  in 
the  telescope,  and  of  course  no  observations  of  spots  are  possible. 

The  inclination  of  the  planet's  equator  to  the  plane  of  its 
orbit  and  the  positions  of  its  poles  and  equinoxes  are  deduced 
from  the  observations  of  the  paths  of  the  spots  as  they  cross  the 
disk.  Such  data,  however,  are  available  only  in  the  cases  of 
Mars,  Jupiter,  and  Saturn. 

It  may  be  added  that  the  disappearance  of  the  variations  of 
the  brightness  of  Eros  in  May,  1901,  after  persisting  over  two 
months,  is  naturally  explained  by  Professor  Pickering  as  due  to 


340 


MANUAL    OF    ASTRONOMY 


Oblateness 
determined 
from  obser- 
vations of 
planet's 
diameters ; 
also  from 
perturba- 
tions of  its 
satellites. 


Planet's 
albedo 
determined 
by  photo- 
metric 
observa- 
tions. 


Spectro- 
scopic 
peculiar- 
ities. 


Surface 
markings 
and  topog- 
raphy. 


the  fact  that  in  May  its  pole  was  turned  towards  us ;  and,  if  so, 
this  gives  us  the  position  of  the  planet's  axis  and  equator. 

The  oblateness,  or  polar  compression,  of  the  planet,  due  to  its 
rotation,  is  found  simply  by  measuring  the  difference  between 
the  polar  and  equatorial  diameters ;  but  the  difference  is  always 
very  small,  so  that  the  percentage  of  its  probable  error  is  rather 
large. 

In  some  cases  also  the  oblateness  can  be  determined  from 
observation  of  the  motion  of  the  nodes  of  the  planet's  satellites. 
'384.  Data  relating  to  the  Light  of  a  Planet.  —  The  bright- 
ness of  the  planet  and  the  reflecting  power  of  its  surface,  or 
albedo,  are  determined  by  observations  with  the  photometer, 
which  is  sometimes  used  direct,  and  sometimes  attached  to  a 
telescope ;  we  have  just  pointed  out  how,  in  one  case  at  least, 
such  observations  may  also  be  available  for  determining  the 
rotation  of  a  planet. 

The  spectroscopic  peculiarities  of  the  planet's  light  are  of  course 
studied  with  a  spectroscope,  and  usually  by  spectroscopic  photog- 
raphy. A  planet  always  shows,  so  far  as  its  brightness  permits, 
the  lines  of  the  solar  spectrum  and,  in  some  cases,  additional 
lines  or  bands  of  its  own,  which  give  information  as  to  the 
constitution  of  its  atmosphere. 

385.  The  Planet's  Surface  Markings  and  Topography.  —  These 
are  studied  with  the  telescope  by  making  careful  notes  and 
drawings  of  the  appearances  and  markings  seen  at  different 
times.  If  the  planet  has  any  well-defined  and  characteristic 
features  by  which  its  rotation  can  be  determined,  it  is  soon 
possible  to  identify  such  as  are  permanent  and  to  chart  them 
more  or  less  perfectly. 

At  present,  however,  Mars  is  the  only  planet  of  which  we  have  been 
able  to  obtain  what  may  be  called  a  real  map,  though  some  preliminary 
chartings  have  been  attempted  for  Venus  and  Mercury.  The  surface 
markings,  which  are  often  very  distinct  and  beautiful  upon  Jupiter,  are  all 
of  a  more  or  less  transient  character. 


THE  PLANETS   IN   GENERAL  341 

Thus  far  photography  has  given  but  little  help  in  the  study  of  planetary 
surfaces.  The  images  formed  even  by  the  largest  telescope  are  too  small 
compared  with  the  "  grain  "  of  the  sensitive  film  ;  and  the  light  of  the 
planet  is  so  feeble  that  long  exposure  is  required,  during  which  the  atmos- 
pheric disturbances  usually  confuse  the  image.  These  difficulties  have  now 
been  partly  overcome,  and  photographs  of  Jupiter  and  Saturn  recently  ob- 
tained by  Barnard  at  Yerkes  Observatory  show  detail  which  rivals  that  of 
the  finest  drawings.  Photographs  of  Mars  made  by  Lowell  at  Flagstaff  and 
by  Todd  in  Chile  during  the  opposition  of  1907  furnished  valuable  con- 
firmation of  visual  observations. 

386.  The  Satellite  Systems.  —  The  principal  data  to  be  deter-  Satellite 
mined  in  respect  to  these  systems  are  the  distances  and  periods  svstems: 
of  the  satellites.  These  are  got  by  micrometric  measures  of  the  determined 


apparent  distance  and  direction  of  each  satellite  from  the  planet;  bv 

or  from  other  satellites,  as  is  now  quite  the  usual  method,  since  observations. 

the  distance  and  direction  between  two  satellites  (which  are 

mere  points  of  light)  can  be  measured  much  more  precisely  than 

between  a  satellite  and  the  center  of  the  large  disk  of  a  planet. 

The  reduction  of  the  observations  in  this  latter  case  is,  however, 

very  complicated. 

In  a  few  cases  the  satellites  present  disks  large  enough  to  be 
measured  and  show  spots  upon  them,  so  that  questions  of  their 
rotation  and  surface  markings  admit  of  discussion.    Also,  where  Diameters. 
there  are  a  number  of  satellites  attending  a  planet,  their  mutual 
perturbations  furnish  a  very  interesting  subject  of  study  and 
make  it  possible  to  determine  their  masses  relative  to  that  of  Masses. 
the  planet. 

With  the   exception  of  our  moon  and  the   outer  satellites  Near 
of  Jupiter  and  Saturn,  all  the  satellites  move  very  nearly  in  satellltes 

move  nearly 

the  plane  of  their  planet  s  equator,  —  so  far  at  least  as  known,  in  plane  of 

since   the   position  of   the   equators   of    Uranus   and   Neptune  Planet's 

has  never  yet  been  ascertained.    Moreover,   all  the   satellites  have  orbits 

except   the    moon,   Hyperion,   and   those   recently  discovered,  nearly 
move  in  orbits  of  very  small  eccentricity,  in  fact,  almost  perfect 
circles.    Laplace  and  Tisserand  have  shown  that  the  "equatorial 


342 


MANUAL   OF   ASTRONOMY 


Remote 
satellites 
move  nearly 
in  plane  of 
planet's 
orbit. 


Humboldt's 
classifica- 
tion of  the 
planets. 


Relative 
accuracy  of 
different 
planetary 
data. 


protuberance"  of  a  planet,  due  to  its  axial  rotation,  would  tend 
to  keep  a  near  satellite  nearly  in  the  equatorial  plane.  The  more 
distant  satellites,  like  the  moon  and  lapetus,  on  the  other 
hand,  move  nearly  in  the  orbital  plane  of  the  planet. 

The  circularity  of  the  satellite  orbits  is  not  yet  accounted 
for. 

387,  Classification  of  Planets.  —  Humboldt  has  classified  the 
planets  in  two  groups,  —  the  "  terrestrial  planets,"  as  he  calls 
them,  and  the  "  major  planets."     The  terrestrial  group  contains 
the  four  planets  nearest  the  sun,  —  Mercury,  Venus,  the  Earth, 
and  Mars.     They  are  all  bodies  of  similar  magnitude,  ranging 
from  3000  to  8000  miles  in  diameter;    not  very  different  in 
density  and  probably  roughly  alike   in  physical   constitution, 
though  probably  also  differing  very  much  in  the  extent,  density, 
and  character  of  their  atmospheres. 

The  four  major  planets  —  Jupiter,  Saturn,  Uranus,  and  Nep- 
tune—  are  much  larger  bodies,  ranging  from  32000  to  90000 
miles  in  diameter ;  are  much  less  dense ;  and,  so  far  as  we  can 
make  out,  present  only  cloud-covered  surfaces  to  our  inspection. 
There  are  strong  reasons  for  supposing  that  they  are  at  a  high 
temperature,  and  that  Jupiter  especially  is  a  sort  of  "  semi-sun  "; 
but  this  is  not  certain. 

As  to  the  asteroids,  the  probability  is  that  they  represent  a 
fifth  planet  of  the  terrestrial  group,  which,  as  has  been  already 
intimated,  failed  somehow  in  its  evolution,  or  else  has  been 
broken  to  pieces. 

Fig.  133  gives  an  idea  of  the  relative  sizes  of  the  planets. 
The  sun  on  the  scale  of  the  figure  would  be  about  a  foot  in 
diameter. 

388.  Tables  of  Planetary  Data.  —  In  the  Appendix  we  present 
tables  of  the  different  numerical  data  of  the  solar  system,  derived 
from  the  best  authorities  and  calculated  for  a  solar  parallax  of 
8".80,  the  sun's  mean  distance  being  therefore  taken  as  92  897000 
miles.     These   tabulated   numbers,  however,  differ   widely  in 


THE   PLANETS   IN   GENERAL 


343 


accuracy.  The  periods  of  the  planets  and  their  distances  in 
astronomical  units  are  very  precisely  known ;  probably  the  last 
decimal  place  in  the  table  may  be  trusted.  Next  in  certainty 
come  the  masses  of  such  planets  as  have  satellites,  expressed  in 
terms  of  the  sun's  mass.  The  masses  of  Venus  and,  especially, 
of  Mercury  are  much  more  uncertain.  The  distances  of  the 
planets  in  miles,  their  masses  in  terms  of  the  earth's  mass,  and 


FIG.  133.  —Relative  Sizes  of  the  Planets 

their  diameters  in  miles,  all  involve  the  solar  parallax  and 
are  affected  by  the  slight  uncertainty  in  its  amount.  For  the 
remoter  planets,  moreover,  diameters,  volumes,  and  densities  are 
subject  to  a  very  considerable  percentage  of  error,  as  explained 
above  (Sec.  379).  The  student  need  not  be  Surprised,  therefore, 
at  finding  serious  discrepancies  between  the  values  given  in 
these  tables  and  those  given  by  other  authorities,  amounting  in 
some  cases  to  ten  per  cent  or  twenty  per  cent,  or  even  more. 
Such  differences  merely  indicate  the  actual  uncertainties  of  our 
knowledge. 


344 


MANUAL   OF   ASTRONOMY 


389.  Sir  John  HerschePs  Illustration  of  the  Dimensions  of  the 
Solar  System.  —  In  his  Outlines  of  Astronomy  Herschel  gives 
the  following  illustration  of  the  relative  magnitudes  and  dis- 
tances of  the  members  of  our  system : 

Choose  any  well-levelled  field.  On  it  place  a  globe  two  feet  in  diameter. 
This  will  represent  the  sun.  Mercury  will  be  represented  by  a  grain  of 
mustard  seed  on  the  circumference  of  a  circle  164  feet  in  diameter  for  its 
orbit;  Venus,  a  pea,  on  a  circle  of  284  feet  in  diameter  ;  the  Earth,  also 
a  pea,  on  a  circle  of  430 ;  Mars,  a  rather  large  pin's  head,  on  a  circle  of 
654  feet;  the  asteroids,  grains  of  sand,  on  orbits  having  a  diameter  of  1000 
to  1200  feet ;  Jupiter,  a  moderate-sized  orange,  on  a  circle  nearly  half  a  mile 
across  ;  Saturn,  a  small  orange,  on  a  circle  of  four-fifths  of  a  mile ;  Uranus, 
a  full-sized  cherry  or  small  plum,  upon  a  circumference  of  a  circle  more 
than  a  mile  in  diameter ;  and,  finally,  Neptune,  a  good-sized  plum,  on  a 
circle  about  2£  miles  in  diameter. 

We  may  add  that  on  this  scale  the  nearest  star  would  be  on 
the  opposite  side  of  the  earth,  8000  miles  away. 


EXERCISES 

1.  What  is  the  mean  daily  gain  of  the  earth  on  Mars  as  seen  from  the 
sun,  i*e.,  the  synodic  motion  of  Mars,  assuming  their  sidereal  periods  as 
365.25  days  for  the  earth,  and  687  days  for  Mars? 

2.  Find  the  synodic  period  of  Venus,  her  sidereal  period  being  225  days. 

3.  Given  the  synodic  period  of  a  planet  as  3  years,  what  is  its  sidereal 
period?  ^^     <  f  of  a  year,  or 

(  1£  years. 

4.  Given  a  synodic  period  of  4  years,  find  the  sidereal  period. 

5.  What  would  be  the  sidereal  period  of  a  planet  which  had  its  synodic 
period  equal  to  the  sidereal?  Ans.    2  years. 

6.  Within  what  limits  of  distance  from  the  sun  must  lie  all  planets  having 
synodic  periods  longer  than   2  years?     (Apply  Kepler's  third  law  after 
finding  the  sidereal  periods  that  would  give  a  synodic  period  of  2  years.) 

Ans     i  °'763  astron.  units,  or    70  950000  miles,  and 
1  1.588  astron.  units,  or  147  500000  miles. 


THE   PLANETS   IN   GENERAL 


345 


7.  A  brilliant  starlike  object  was  seen  about  7  P.M.  on  May  1  exactly  at 
the  east  point  of  the  horizon.     Could  it  have  been  one  of  the  planets? 
If  not,  why  not  ? 

8.  Mercury  was  at   inferior   conjunction  on   Feb.   8,  1896,  at  1  P.M. 
On  May  6,  at  15  minutes  after  noon  (exactly  one  sidereal  period  later), 
its  elongation  from  the  sun  was  observed  to  be  18°  50'  E.     Find  the  dis- 
tance of  the  planet  from  the  sun  in  astronomical  units,  the  earth's  orbit 
being  regarded  as  circular.     (See  Sec.  371.) 

(The  fact  that  the  first  observation  was  made  at  conjunction  greatly 

simplifies  the  calculation.)        ,  TV  ,          ,. 

>        <  Distance  from  the  sun,  0.335  astron.  units. 

(.  (The  planet  was  near  perihelion.) 

9.  At  a  time  when  Jupiter's  distance  from  the  earth  was  4.6  astronomi- 
cal units  its  apparent  equatorial  diameter  was  observed  to  be  43". 3.     Find 
the  diameter  in  miles  as  determined  by  this  observation. 

Ans.    89700  miles. 


New  Physical  Observatory,  Greenwich 


CHAPTER   XIII 
THE   TERRESTRIAL  AND   MINOR  PLANETS 

Mercury,  Venus,  and  Mars  —  The  Asteroids  —  Intramercurial  Planets  —  =• 
:  Zodiacal  Light 

MEKCUKY 

390.   Mercury  has  been  known  from  remote  antiquity,  and 
we  have  recorded  observations  running  back  to  264  B.C.     At 
first  astronomers  failed  to  recognize  it  as  the  same  body  on  the 
eastern  and  western  side  of  the  sun,  and  among  the  Greeks  it 
Two  names    had  for  a  time  two  names,  —  Apollo  when  morning  star,  and 
for  Mercury.  ]y[ercury  when  evening  star.     It  is  so  near  the  sun  that  it  is 
comparatively  seldom  seen  with  the  naked  eye  (Copernicus  is 
said  never  to  have  seen  it),  but  when  near  its  greatest  elonga- 
tion it  is  easily  enough  visible  as  a  brilliant  star  of  the  first  mag- 
Best  times      nitude,  though  always  low  down  in  the  twilight.     It  is  best 
seen  *n  ^e  even^ng  a^  such  eastern  elongations  as  occur  in  March 
and  April.     As  a  morning  star  it  is  best  seen  at  western  elonga- 
tions in  September  and  October. 

It  is  an  exceptional  planet  in  various  ways.  It  is  the  nearest 
to  the  sun,  receives  the  most  light  and  heat,  is  the  swiftest  in  its 
movement,  and  (excepting  some  of  the  asteroids)  has  the  most 
eccentric  orbit,  with  the  greatest  inclination  to  the  ecliptic.  It  is 
also  the  smallest  in  diameter  (again  excepting  the  asteroids)  and 
has  the  least  mass. 

Peculiarities  391.  Its  Orbit.  —  Its  mean  distance  from  the  sun  is  about 
of  Mercury's  36000000  miles,  but  the  eccentricity  of  its  orbit  is  so  great 
tk)naiinmany  (0.205)  that  the  £uii  is  7500000  miles  out  of  the  center,  and 


respects.        the  distance  of  the  planet  from  the  sun  ranges  all  the  way  from 

346 


THE   TERRESTRIAL   AND   MINOR  PLANETS  347 

28  500000  to  43  500000,  while  the  velocity  in  its  orbit  varies 
from  36  miles  a  second  at  perihelion  to  only  23  at  aphelion. 
Its  distance  from  the  earth  ranges  from  about  50  000000  miles 
at  the  most  favorable  inferior  conjunction  to  about  136  000000 
at  the  remotest  superior  conjunction. 

A  given  area  upon  its  surface  receives  on  the  average  nearly 
seven  times  as  much  light  and  heat  as  the  same  area  on  the 
earth ;  and  the  heat  received  at  perihelion  is  greater  than  that 
at  aphelion  in  the  ratio  of  9:4.  For  this  reason,  even  if  the 
planet's  equator  should  be  found  to  be  parallel  to  the  plane  of 
its  orbit,  there  must  be  two  seasons  in  each  Mercurian  year,  Seasons  due 
due  to  the  changing  distance;  and  if  the  planet's  equator  is  tothe 

•      i  •        i  T  T  -i  eccentricity 

inclined  nearly  at  the  same  angle  as  ours,  the  seasons  must  be  Of  its  orbit, 
extremely  complicated. 

The  sidereal  period  is  88  days,  and  the  synodic  period  (from 
conjunction  to  conjunction)  116  days.  The  greatest  elongation 
ranges  from  18°  to  28°,  on  account  of  the  eccentricity  of  its 
orbit,  and  occurs  about  22  days  before  and  after  inferior  conjunc- 
tion. The  inclination  of  the  orbit  to  the  ecliptic  is  about  7°. 

392.   The  Planet's  Magnitude,   Mass,   etc The    apparent  Diameter, 

diameter  of  Mercury  ranges  from  5"  to  about  13",  according  to  mass'  etc*' 

of  Mercury. 

its  distance  from  us,  and  the  real  diameter  is  very  nearly  3000 
miles.  Its  surface  is  about  one  seventh  that  of  the  earth,  and  its 
volume,  or  bulk,  one  eighteenth. 

The  planet's  mass  is  not  accurately  known ;  it  is  very  difficult 
to  determine,  since  it  has  no  satellite,  and  it  is  so  near  the  sun 
that  its  disturbing  effect  upon  the  other  planets  is  extremely 
small,  so  that  the  values  calculated  from  perturbations  produced 
by  it  are  very  discordant.  Different  computers  give  results  rang- 
ing all  the  way  from  ^  of  the  earth's  mass  to  •£•$.  It  probably  lies 
somewhere  between  -^  and  -fa.  Its  mass  is,  however,  unques- 
tionably smaller  than  that  of  any  other  planet,  asteroids  excepted. 

Our  uncertainty  as  to  its  mass  prevents  us  from  assigning  Small  sur- 
any  certain  values  to  its  density  or  surface  gravity  ;  probably  it  facesravity- 


348 


MANUAL   OF   ASTRONOMY 


Telescopic 
appearance 
and  phases. 


is  not  quite  so  dense  as  the  earth.  Assuming  Newcomb's  mass 
of  ^L.  that  of  the  earth,  the  density  comes  out  about  0.85,  and 
its  surface  gravity  a  little  less  than  1. 

393.  Telescopic  Appearances,  Phases,  etc.  —  In  the  telescope 
the  planet  looks  like  a  little  moon,  showing  phases  precisely 
similar  to  those  of  the  moon.  At  inferior  conjunction  the  dark 
side  is  towards  us,  at  superior  conjunction  the  illuminated  sur- 
face. At  greatest  elongation  the  planet  appears  as  a  half-moon. 


FIG.  134.  — Phases  of  Mercury  and  Venus 

It  is  gibbous  between  superior  conjunction  and  greatest  elonga- 
tion, while  between  inferior  conjunction  and  elongation  it  shows 
the  crescent  phase. 

Fig.  134  illustrates  the  phases  of  Mercury  (and  of  Venus  also). 
Atmosphere  The  atmosphere  of  the  planet  cannot  be  as  dense  as  that  of 
of  Mercury.  yenus?  because  at  a  transit  across  the  sun  it  shows  no  encircling 
ring  of  light,  as  Venus  does  (Sec.  401).  Both  Huggins  and 
Vogel,  however,  report  spectroscopic  observations  which  imply 
the  presence  of  water  vapor ;  i.e.,  the  planet's  spectrum,  in  addi- 
tion to  the  ordinary  dark  lines  belonging  to  the  spectrum  of 
reflected  sunlight,  shows  other  bands  known  to  be  due  to  water 
vapor,  but  it  is  not  yet  quite  certain  whether  the  vapor  is  in 
the  planet's  atmosphere  or  in  our  own.  On  the  whole,  it  is 
probable  that  the  atmospheric  conditions  are  much  like  those 
upon  the  moon,  since  under  the  powerful  action  of  the  solar 


THE  TERRESTRIAL  AND  MINOR  PLANETS 


349 


heat  a  planet  of  so  small  a  mass  would  probably  lose  most  of  its 
atmosphere,  if  it  ever  possessed  any. 

Generally  the  planet  is  so  near  the  sun  that  it  can  be  observed 
only  by  day,  but  when  proper  precautions  are  taken  to  screen 
the  object-glass  from  direct  sunlight,  its  observation  is  not  spe- 
cially difficult.  The  surface  presents  very  little  of  interest  to 
an  ordinary  telescope.  Like  the  moon,  it  is  brighter  at  the  edge 
than  at  the  center, 
but  until  recently  no 
markings  have  been 
observed  upon  its 
disk  well  enough  de- 
nned to  give  us  any 
trustworthy  infor- 
mation as  to  its 
geography  or  even 
its  rotation. 

394.  The  Planet's 
Rotation. — Schroter, 
a  German  astrono- 
mer and  a  contempo- 
rary of  Sir  William 
Herschel,  and,  to 
speak  mildly,  an  im- 
aginative man,  early 
in  the  last  century  reported  certain  observations  which  he  con- 
sidered to  indicate  high  mountains  on  the  planet  and  deduced 
a  rotation  period  of  24h5m,  —  a  result  that  stood  uncontradicted 
until  about  1890  and  still  appears  in  many  text-books,  though 
unconfirmed  by  other  observers  with  instruments  certainly  much 
better  than  his. 

In  1889  the  Italian  astronomer,  Schiaparelli,  announced  the 
discovery  upon  the  planet  of  certain  dark  permanent  markings,  of 
which  he  presented  a  map  (Fig.  135).  He  found  also  that  these 


Planet  best 
observed 
with  the 
telescope 
in  daytime. 


FIG.  135.  —  Mercury 
After  Schiaparelli 


The  planet 
in  its 
rotation 
keeps  the 
same  face 
always 
turned 
towards 
the  sun. 


350  MANUAL   OF   ASTRONOMY 

markings  did  not  change  their  positions  upon  the  planet's  disk 
even  in  the  course  of  several  hours  (a  fact  obviously  inconsistent 
with  rotation  in  twenty-four  hours),  but  remained  always 
nearly  fixed  in  their  position  with  respect  to  the  "termi- 
nator,"-—the  boundary  between  the  illuminated  and  unillumi- 
nated  hemispheres  of  the  planets.  Granting  this  permanency, 
it  follows  that  the  planet  rotates  on  its  axis  only  once  during 
its  orbital  period  of  eighty-eight  days;  i.e.,  it  keeps  the  same 
face  always  towards  the  sun  as  the  moon  does  towards  the 
earth.  Slight  changes  in  the  positions  of  the  spots  show,  how- 
Large  libra-  ever,  a  comparatively  large  libration  in  longitude  (Sec.  203,  (2)), 
as  there  ought  to  be,  considering  the  great  eccentricity  of  the 
planet's  orbit.  This  libration  amounts  to  about  23^° ;  i.e.,  the 
sun,  seen  from  a  favorable  position  on  the  planet,  instead  of 
rising  and  setting  as  with  us,  must  seem  to  oscillate  east  and 
west  in  the  sky  to  the  extent  of  47°  in  a  period  of  eighty- 
eight  days. 

Schiaparelli's  reported  discovery  excited  great  interest,  but  the  observa- 
tions are  extremely  difficult  even  under  the  Italian  atmosphere,  and  confir- 
mation was  tardy.  In  1896,  however,  Mr.  Lowell  reported  its  complete 
corroboration  as  the  result  of  observations  at  his  Flagstaff  Observatory, 
though  it  is  rather  difficult  to  reconcile  his  drawings  of  the  surface  mark- 
ings with  those  of  Schiaparelli.  Partial  confirmations  have  also  been 
received  from  other  quarters. 

If  this  rotation  period  is  correct,  as  it  probably  is,  one  face  of 
the  planet  is  always  sunless  and  probably  intensely  cold,  while 
the  opposite  is  always  exposed  to  a  sevenfold  African  blaze  of 
sunbeams.  Between  these  regions  is  a  space  in  which,  as  a 
consequence  of  librations,  the  sun  alternately  rises  above  the 
horizon  and  drops  back  again. 

Albedo  ex-         395,    Albedo. —  The  reflecting  power  of  the  planet's  surface 
tremeiyiow.  ig  very  low?  —  according  to  Zollner,  0.13,  a  little  less  than  that 
of  the  moon  and  much  below  that  of  any  other  planet,  hardly 
higher  than  that  of  a  darkish  granite. 


THE   TERRESTRIAL   AND   MINOR   PLANETS  351 

In  the  proportion  of  light  given  out  at  its  different  phases  it 
behaves  like  the  moon,  flashing  out  strongly  near  the  "full," 
i.e.,  near  superior  conjunction, — a  fact  which  probably  indicates 
a  rough  surface  with  very  little  atmospheric  absorption  of 
light. 

396.   Transits  of  Mercury.  —  At  the  time  of  inferior  conjunc-  Transits  of 
tion  the  planet  usually  passes  north  or  south  of  the  sun,  the  Mercurv m 
inclination  of  its  orbit  being  7° ;  but  if  the  conjunction  occurs  November, 
when  the  planet  is  very  near  its  node,  it  crosses  the  disk  of  the  May  transits 
sun  as  a  small  black  spot,  —  not,  however,  large  enough  to  be 
seen  without  a  telescope.     Since  the  earth  passes  the  planet's 
node  on  May  7  and  November  9,  transits  can  occur  only  near 
those  dates. 

If  the  planet's  orbit  were  truly  circular,  the  transit  limit 
(corresponding  to  the  ecliptic  limit,  Sees.  286  and  293)  would 
be  2°  10',  and  the  conditions  of  transit  would  be  the  same  at 
each  node ;  but  at  the  May  transits  the  planet  is  near  its  aphe- 
lion and  exceptionally  near  the  earth,  so  that  the  May  transits 
are  only  about  half  as  numerous  as  the  other. 

For  the  November  transits  the  interval  is  sometimes  only  intervals 
7  years,  but  is  usually  13  or  46  years.  For  the  May  transits  the 
7-year  interval  is  impossible.  Twenty-two  synodic  periods  of 
Mercury  are  pretty  nearly  equal  to  7  years ;  41  much  more 
nearly  equal  to  13  years,  and  145  are  almost  exactly  equal  to 
46  years.  Hence,  46  years  after  a  given  transit  another  one  at 
the  same  node  is  almost  certain. 

The  last  transit  completely  visible  in  the  United  States  was  in  November, 
1894.  During  the  first  half  of  the  present  century  transits  will  occur  as 
follows : 

Nov.  14,  1907,  May  7,  1924,  May  10,  1937, 

Nov.    7,  1914,  Nov.  8,  1927,  Nov.  12,  1940. 

Only  the  two  first  of  these  will  be  visible  in  the  United  States,  and  not 
the  entire  transit  in  either  case.  The  first  transits  of  which  the  whole  will 
be  visible  here  occur  on  Nov.  13,  1953,  and  Nov.  6,  1960. 


352 


MANUAL   OF   ASTRONOMY 


Transits  of 
Mercury  a 
test  of  uni- 
formity of 
earth's 
rotation. 


Transits  of  Mercury  are  of  no  special  astronomical  impor- 
tance, except  as  furnishing  accurate  determinations  of  the 
planet's  place. 

Newcomb  has  made  a  thorough  examination  of  all  the 
recorded  transits  in  order  to  test  the  uniformity  of  the  earth's 
rotation.  They  appear  to  indicate  certain  small  irregularities 
in  it,  but  hardly  establish  the  fact  as  absolutely  certain. 


Brilliance  of 
Venus. 


Peculiarities 
of  orbit  of 
Venus.    Its 
eccentricity 
smaller  than 
that  of  any 
other  planet. 


VENUS 

The  next  planet  in  order  from  the  sun  is  Venus,  by  far  the 
brightest  and  most  conspicuous  of  all,  —  the  earth's  twin  sister 
in  magnitude,  density,  and  general  constitution,  if  not  in  other 
physical  conditions.  Like  Mercury,  it  had  two  names  among 
the  Greeks, —  Phosphorus  as  morning  star,  and  Hesperus  as 
evening  star. 

It  is  so  brilliant  that  it  is  easily  seen  by  the  naked  eye  in  the 
daytime  for  several  weeks  when  near  its  greatest  elongation ; 
occasionally  it  is  bright  enough  to  catch  the  eye  at  once,  but 
usually  is  seen  by  daylight  only  when  one  knows  precisely 
where  to  look  for  it. 

397.  Distance,  Period,  and  Inclination  of  Orbit.  —  Its  mean 
distance  from  the  sun  is  67  200000  miles. 

The  eccentricity  of  the  orbit  is  the  smallest  in  the  planetary 
system  (only  0.007),  so  that  the  whole  variation  of  its  distance 
from  the  sun  is  less  than  a  million  miles. 

Its  orbital  velocity  is  22  miles  per  second. 

The  heat  and  light  received  from  the  sun  are  most  exactly 
double  the  amount  received  by  the  earth. 

Its  sidereal  period  is  225  days,  or  nearly  seven  and  one-half 
months,  and  its  synodic  period  584  days,  —  a  year  and  seven 
months.  From  superior  conjunction  to  elongation  on  either 
side  is  220  days,  while  from  inferior  to  elongation  it  is  only 
72  days, — less  than  one  third  as  long. 


THE   TERRESTRIAL   AND   MINOR   PLANETS  853 

The  greatest  elongation  is  47°  or  48°. 
The  inclination  of  its  orbit  is  about  3£°. 

398,  Magnitude,  Mass,  Density,  etc The  apparent  diameter  Diameter. 

of  the  planet  ranges  from  67 "  at  the  time  of  inferior  conjunction  "iass/ 

to  only  11"  at  superior  conjunction,  the  great  difference  depend-  surface' 
ing  upon  the  enormous  variation  in  the  distance  of  the  planet  sravity»  etc 
from  the  earth,  which  is  only  26  000000  miles  at  inferior  conjunc- 
tion and  160  000(500  at  superior.     The  real  diameter  of  the  planet 
is  about  7600  miles,  according  to  the  recent  measures  of  See  at 
Washington. 

According  to  this,  its  surface,  compared  with  that  of  the 
earth,  is  0.91 ;  its  volume,  0.87.  (These  numbers  differ  some- 
what from  those  given  in  the  tables  in  the  Appendix,  which  are 
allowed  to  stand  unchanged,  as  illustrating  the  discrepancies 
between  good  authorities  in  such  cases.) 

By  means  of  the  perturbations  she  produces  upon  the  earth, 
the  mass  of  Venus  is  found  to  be  a  little  more  than  four  fifths 
(0.82)  of  the  earth's;  hence,  her  density  is  about  ninety-four 
per  cent  and  her  superficial  gravity  ninety  per  cent  of  the 
earth's.  A  man  who  weighs  160  pounds  here  would  weigh 
about  140  pounds  on  Venus. 

399.  Phases.  —  The  telescopic  appearance  of  the  planet  is  Phases  of 
striking  on  account  of  her  great  brilliance.     When  midway  Venus- 
between  greatest  elongation  and  inferior  conjunction  she  has  an 
apparent  diameter  of  40",  so  that,  with  a  magnifying  power  of 

only  45,  she  looks  exactly  like  the  moon  four  days  old,  and  of 
precisely  the  same  apparent  size,  though  very  few  persons  would 
think  so  on  first  viewing  the  planet  through  a  telescope.  The 
novice  always  underrates  the  apparent  size  of  a  telescopic 
object,  because  he  instinctively  adjusts  his  focus  as  if  looking 
at  a  picture  or  a  page  only  a  few  inches  away,  instead  of  pro- 
jecting the  object  visually  into  the  sky. 

According  to  the  theory  of  Ptolemy,  Venus  could  never 
show  us  more  than  half  her  illuminated  surface,  since,  according 


354 


MANUAL   OF   ASTRONOMY 


Phases  irrec-  to  his  hypothesis,  she  was  always  between  us  and  the  supposed 
withPtde  or^  °f  ^e  sun'  Accordingly,  when  in  1610  Galileo  discovered 
maic  with  his  newly  invented  telescope  that  she  exhibited  the 

system.         gMous  phase  as  well  as  the  crescent,  it  was  a  strong  argu- 
ment for  the  Copernican  theory. 


Galileo's 
discovery 
of  the 
phases. 


Galileo  announced  his  discovery  in  a  curious  way,  by  publishing  the 

anagram,  — 

Haec  immatura  a  me  iam  f rustra  leguntur ;  o.  y. 

Some  months  later  he  furnished  a  translation,  which  is  found  by  merely 
transposing  the  letters  of  the  anagram  and  reads,  "  Cynthiae  figuras  aemu- 
latur  Mater  Amorum,"  meaning  "  The  Mother  of  the  Loves  (Venus)  imi- 
tates the  phases  of  Cynthia,"  i.e.,  of  the  moon. 


Fia.  136.  —  Telescopic  Appearances  of  Venus 

Fig.  136  represents  the  disk  of  the  planet  as  seen  at  five 
points  in  its  orbit.  1,  3,  and  5  are  taken  respectively  at 
superior  conjunction,  greatest  elongation,  and  near  inferior  con- 
junction, while  2  and  4  are  at  intermediate  points.  Number  2 
is  badly  engraved,  however;  the  sharp  corners  are  impossible 
since  the  terminator  is  always  a  semi-ellipse  (Sec.  205V 


THE   TERRESTRIAL   AND   MINOR  PLANETS 


356 


The  planet  attains  its  maximum  brightness  thirty-six  days 
before  and  after  inferior  conjunction,  at  a  distance  of  about  38° 
or  39°  from  the  sun,  when  its  phase  is  like  that  of  the  moon 
about  five  days  old.  It  then  casts  a  strong  shadow  and,  as 
already  said,  is  easily  visible  by  day  with  the  naked  eye. 

400.  Albedo.  —  According  to  Zollner,  the  albedo  of  the  planet  High  albedo 
is  0.50,  which  is  about  three  times  that  of  the  moon  and  almost  of  Venus- 
four  times  that  of  Mer- 
cury.    It  is,  however,  ex- 
ceeded by  the  reflecting 

power  of  the  surface  of 
Jupiter  and  Uranus,  while 
that  of  Saturn  appears  to 
be  about  the  same. 

This  high  reflecting 
power  probably  indicates 
that  the  surface  is  mostly 
covered  with  cloud,  as 
few  rocks  or  soils  could 
match  it  in  brightness. 

Lowell,  however,  de- 
nies the  existence  of  any- 
thing like  a  continuous 
cloud  veil  such  as  has 
been  generally  supposed. 

401.  Atmosphere  of  the  Planet.  —  There  is  no  question  that 
this  planet  has  an  atmosphere  of  considerable  density. 

When  the  planet  is  entering  upon  the  sun's  disk,  or  leaves 
it  at  a  "transit,"  the  portion  of  the  disk  outside  the  sun  is 
encircled  by  a  beautiful  ring  of  light,  due  to  the  refraction, 
reflection,  and  dispersion  of  light  by  the  planet's  atmosphere 
(Fig.  137).  If  it  were  due  solely  to  refraction,  it  would  indi- 
cate that  this  atmosphere,  according  to  the  computations  of 
Watson  and  others,  must  have  an  elevation  of  some  66  miles 


FIG.  137.  —  Atmosphere  of  Venus  as  seen  during 

the  Transit  of  1882 

Vogel 


866 


MANUAL   OF   ASTRONOMY 


Bright  ring 
surrounding 
planet's 
disk  due  to 
reflection 
and  diffusion 
of  light 
rather  than 
to  refrac- 
tion. 


Density  of 
the  atmos- 
phere of 
Venus. 


Question  as 
to  presence 
of  water 
vapor. 

Unexplained 
light  on 
planet's 
surface. 


and  be  considerably  denser  than  our  own;  but  this  conclusion 
is  very  doubtful. 

When  the  planet  is  near  the  sun,  about  the  time  of  inferior 
conjunction,  the  horns  of  its  crescent  extend  notably  beyond 
the  diameter,  and  when  very  near  the  sun  they  can  be  seen, 
by  carefully  screening  the  object-glass  of  the  telescope  from 
the  sunlight,  to  form  a  complete  ring  around  the  disk,  as 
observed  by  Professor  Lyman  of  New  Haven  and  others  in 
1860  and  1874.  This  phenomenon,  which  is  unquestionable, 
has  usually  been  ascribed  to  refraction;  but  the  observations 
of  Russell  at  Princeton  in  1898  showed  that  it  must  be  due 
mainly  to  diffuse  reflection  of  light  by  the  planet's  atmosphere, 
like  that  which  causes  our  twilight,  and  that  refraction  proper 
plays  only  a  very  secondary  part. 

If  the  ring  were  due  to  refraction,  as  by  a  lens,  the  widest 
and  brightest  part  of  it  should  be  on  the  side  of  the  planet 
most  distant  from  the  sun,  where  the  rays  would  be  bent  towards 
the  observer,  and  not  on  the  side  next  the  sun,  as  is  actually  and 
conspicuously  the  case.  On ,  this  side  refracted  rays  are  bent 
away  from  the  observer  and  would  not  reach  his  eye,  while 
reflected  rays  are  thrown  towards  it. 

The  same  observations  also  cast  doubt  on  the  hitherto  accepted 
conclusion  as  to  the  great  density  of  the  atmosphere,  making  it 
probable  that  it  is  somewhat  rarer  than  our  own,  rather  than 
much  denser;  and  this  might  be  expected,  considering  the 
planet's  smaller  mass  and  presumably  higher  temperature. 

The  presence  of  water  vapor  in  the  planet's  atmosphere  has  been 
announced  by  several  of  the  earlier  spectroscopic  observers.  The  evidence, 
however,  is  hardly  conclusive. 

Another  curious  phenomenon,  not  very  satisfactorily  explained  as  yet,  is 
the  occasional  appearance  of  light  on  the  unilluminated  part  of  the  planet's 
surface,  making  the  whole  disk  visible,  like  the  new  moon  in  the  old 
moon's  arms.  This  light  cannot  be  accounted  for  by  any  effect  of  sunlight, 
but  must  originate  on  the  planet's  surface  or  in  her  atmosphere.  It  recalls 
the  aurora  borealis  of  the  earth  and  other  electrical  manifestations. 


THE    TERRESTRIAL    AND    MINOR   PLANETS 


357 


Surface 
markings. 


402.    Surface  Markings.  —  The  surface  of  the  planet  is  so 
brilliant  as  seen  in  the  telescope  that  it  is  very  difficult  to  make 
out  any  markings  upon  it ;  indeed,  it  is  generally  best  in  study- 
ing the  surface  to  use  a  light  shade  glass.     The  disk  is  brightest 
at  the  limb,  but  the  light  fades  off  rapidly  at  the  terminator, 
and  over  the  surface  there  have  been  made  out  indistinct  patches 
of  less  or  greater  brightness,  as  shown  in  Fig.  138,  from  draw- 
ings by  Mascari  made  at  the  observatory  on  Mt.  Etna  in  1895, 
—  an  excellent  representation  of  the  planet's  usual  appearance. 
The  darkest  shadings  may  possibly  be  continents  and  oceans, 
dimly  visible,  though  their  comparative  permanence  with  respect 
to  the  terminator 
makes  this  ques- 
tionable;    more 
probably  they  are 
purely    atmos- 
pheric   effects. 
But  observations 
are  as  yet  hardly 
decisive. 

Occasionally 

very  bright  spots  appear  at  the  ends  of  the  terminator,  which  Polar  caps, 
may  possibly  be  polar  caps  like  those  of  Mars,  and,  if  so,  show 
that  the  planet's  axis  must  be  nearly  perpendicular  to  its  orbit. 
On  the  terminator  roughnesses  and  irregularities  are  sometimes 
seen  which  may  perhaps  be  due  to  mountains,  to  some  of  which 
Schroter  assigned  extravagant  elevations  exceeding  20  miles. 

Lowell,  in  1898,  in  opposition  to  all  previous  observers,  re- 
ported the  discovery  of  permanent  markings  consisting  of  rather 
narrow,  nearly  straight,  dark  streaks,  radiating  like  spokes  from 
a  sort  of  central  hub.  He  describes  them  as  fairly  definite  in 
outline,  but  dim,  as  if  seen  through  a  luminous  but  unclouded 
atmosphere  of  considerable  depth ;  and  he  goes  so  far  as  to  give 
a  map  of  the  planet,  with  names  attached  to  some  of  the  leading 


FIG.  138.  — Venus 
After  Mascari 


Surface 
markings 
according 
to  Lowell. 


358 


MANUAL  OF  ASTRONOMY 


Rotation : 
probably 
planet  keeps 
same  face 
towards 
sun,  like 
Mercury. 


Possible 
decision  by 
the  spectro- 
scope. 


features.  His  observations  have  been  confirmed  by  other  observ- 
ers at  Flagstaff.  Fig.  139  is  from  one  of  his  drawings. 

403.  Rotation,  Position  of  Axis,  etc.  —  The  earlier  observers, 
from  the  first  Cassini  in  1666  down  to  De  Vico  in  1841,  assigned 
to  the  planet  a  rotation  period  of  about  23h21m, — uncontra- 
dicted,  it  is  true,  but  regarded  with  a  good  deal  of  distrust, 
because  the  observations  were  of  spots  extremely  vague  and 
indistinct  and  were  not  very  accordant. 

Some  highly  respected  authorities  still  accept  this  period,  but 
the  general  opinion  of  astronomers  now  concurs  with  the  con- 
clusion of  Schiaparelli,  who  considers  that  his  observations  make 
it  certain  that  the  rotation  must  be  very  slow,  and  render  it 


FIG.  139.  —  Venus 
From  drawings  of  P.  Lowell 

highly  probable  that  Venus  follows  the  example  of  Mercury  in 
keeping  the  same  face  always  towards  the  sun,  having,  therefore, 
a  diurnal  period  of  225  days.  This  is  confirmed  by  Perrotin  at 
Nice,  and  by  Lowell  at  the  Flagstaff  Observatory,  and  by  several 
other  observers. 

It  is  probable  that  the  spectroscope  will  ultimately  settle  the 
question  (though  the  observation  will  be  very  difficult)  by  show- 
ing, according  to  the  Doppler  principle  (Sec.  254),  how  fast  the 
eastern  and  western  edges  of  the  planet's  disk  respectively 
advance  and  recede  ;  the  observation  has  already  been  attempted 
at  Pulkowa,  and  at  the  Lick,  Yerkes,  and  Flagstaff  observatories. 
The  results  so  far  are  not  conclusive,  but  on  the  whole  rather 
favor  the  longer  period. 


THE   TERRESTRIAL   AND   MINOR   PLANETS  359 

On  the  other  hand,  the  planet  shows  no  sensible  oblateness,  as  No  measur- 
it  should  if  it  had  a  day  of  the  same  length  as  the  earth's;  if  ableoblate- 

*  ness. 

that  were  the  case,  there  should  be  a  difference  of  nearly  i" 
between  the  equatorial  and  polar  diameters,  which  has  never 
been  observed. 

The   inclination  of  the  planet's   equator  cannot  be  exactly  inclination 
determined,  but  it  is  almost  certain  that  it  must  nearly  coincide  of  e(iuator 

J  to  orbit 

with  the  plane  of  its  orbit.     The  old  determination  of  De  Vico,  probably 
still  found  in  many  text-books,  making  the  inclination  37°,  is  smalL 
certainly  erroneous. 

404,  Question  of  Satellite. — No  satellite   has  yet  been  dis-  NO  satellite, 
covered,  and  it  is  certain  that  the  planet  has  none  of  any  con- 
siderable size.     It  is  not  impossible,  however,  that  it  may  have 

some  pygmy  attendant,  like  those  of  Mars,  since  the  great 
brilliance  of  the  planet  and  its  nearness  to  the  sun  would  make 
the  discovery  of  such  a  body  extremely  difficult.  There  have 
been  in  the  past  several  announcements  of  a  satellite ;  but  not 
one  has  been  verified,  and  most  of  them  were  mistakes,  since 
explained,  either  as  observations  of  stars,  or  by  reflections  in 
the  eyepiece  of  the  observer's  telescope. 

405.  Transits.  —  Occasionally    Venus    passes    between    the  Transits, 
earth    and    the    sun    at   inferior   conjunction   and    "transits," 

or  crosses,  the  disk  of  the  sun  from  east  to  west  as  a  round 
black  spot,  easily  seen  by  the  naked  eye  through  a  suitable 
shade  glass.     When  the  transit  is  central  it  occupies  about 
eight  hours,  but  when  the  track  is  near  the  edge  of  the  disk 
it  is  correspondingly  shortened.     Since  the  transit  can  occur  Transit 
only  when  the  sun  is  within  about  4°  of  the  node,  the  phe-  ^^d 
nomenon  is  rare  and  can  happen  only  within  a  day  or  two  December, 
of  the  dates  when  the  earth  passes  the  nodes,  viz.,  June  5  and 
December  7. 

The  special  interest  of  the  transits  lies  in  their  availablity 
for  the  purpose  of  finding  the  parallax  and  distance  of  the  sun, 
as  first  pointed  out  by  Halley  in  1679. 


360 


MANUAL   OF   ASTRONOMY 


Importance          The  earliest  observed  transit  in  1639  was  seen  by  two  persons  only 
of  determin-    (Horrocks   and   Crabtree,   in   England),   but  the  four  which   have  since 


ing  the 
solar  paral- 
lax. 


Recurrence 
and  dates  of 
transits. 


Transits  at 

present 

come  in 

pairs. 

Solitary 

transits 

possible. 


occurred,  in  June,  1761  and  1769,  and  in  December,  1874  and  1882,  were 
extensively  observed  by  scientific  expeditions  sent  out  by  the  different 
governments  to  all  parts  of  the  world  where  they  were  visible.  The 
transits  of  1769  and  1882  were  visible  in  this  country. 

It  is,  however,  hardly  likely  that  so  much  trouble  and  expense  will  be 
hereafter  expended  upon  observations  of  transits.  Other  methods  of 
determining  the  solar  parallax  have  been  found  to  be  more  trustworthy. 

406.  Recurrence  and  Dates  of  Transits.  —  Five  synodic  revolu- 
tions of  Venus  are  very  nearly  equal  to  eight  years,  the  differ- 
ence being  little  more  than  one  day;  and  still  more  nearly,— 
in  fact,  almost  exactly,  —  243  years  are  equal  to  152  synodic 
revolutions.  If,  then,  we  have  a  transit  at  any  time,  another 
may  occur  at  the  same  node  eight  years  earlier  or  later.  Sixteen 
years  before  or  after  it  will  be  impossible,  and  no  other  transit 
can  then  occur  at  the  same  node  until  after 
the  lapse  of  235  or  243  years,  though  a 
transit  or  pair  of  transits  may,  and  usually 
will,  occur  at  the  other  node  in  about  half 
that  time :  thus,  the  next  pair  of  transits 
of  Venus  will  occur  on  June  8,  2004,  and 
June  6,  2012. 

If  the  planet  crosses  the  sun  nearly  cen- 
trally, the  transit  will  be  "solitary,"  i.e.,  not 
accompanied  by  another  eight  years  before 
or  after.  If,  however,  the  track  is  more  than  1 2'  from  the  sun's 
center,  it  will  be  accompanied  by  another  at  eight  years  interval. 
At  present  transits  come  thus  in  pairs  and  have  been  doing  so 
for  several  centuries ;  after  a  time  this  will  cease  to  be  the  case, 
and  they  will  become  solitary  for  another  long  period. 

Fig.  140  shows  the  tracks  of  Venus  across  the  sun's  disk  in 
1874  and  1882. 


FIG.  140.  —  Transit  of 
Venus  Tracks 


THE   TERRESTRIAL   AND   MINOR   PLANETS  361 

MAES 

407,  This  planet,  like  Mercury  and  Venus,  is  prehistoric  as  Mars:  data 
to  its  discovery.     It  is  so  conspicuous  in  color  and  brightness  relatmsto 
and  in  the  extent  and  apparent  capriciousness  of  its  movement 

among  the  stars,  that  it  could  not  have  escaped  the  notice  of  the 
very  earliest  observers. 

Its  mean  distance  from  the  sun  is  a  little  more  than  one  and 
a  half  times  that  of  the  earth  (141  500000  miles),  and  the  eccen- 
tricity of  its  orbit  is  so  considerable  (0.093)  that  its  radius  vector 
varies  more  than  26  000000  miles. 

At  opposition  the  planet's  average  distance  from  the  earth  is 
48  600000  miles.  When  opposition  occurs  near  the  planet's 
perihelion  this  distance  is  reduced  to  35  500000  miles,  while 
near  aphelion  it  is  over  61  000000.  At  superior  conjunction 
the  average  distance  from  the  earth  is  234  000000. 

The  apparent  diameter  and  brilliancy  of  the  planet  vary  enor-  Enormous 
mously  with  those  great  changes  of  distance.     At  a  favorable  ™natlon  °* 
opposition  (when  the  distance  is  at  its  minimum)  the  planet  is  brightness, 
more  than  fifty  times  as  bright  as  at  superior  conjunction  and 
fairly  rivals  Jupiter ;  when  most  remote  it  is  hardly  as  bright  as 
the  pole-star. 

The  favorable  oppositions  occur  always  in  the  latter  part  of  August  (at   Favorable 
which  time  the  earth  as  seen  from  the  sun  passes  the  perihelion  of  the   oppositions, 
planet)   and  at  intervals  of  fifteen  or  seventeen  years.     The  last  such 
opposition  was  in  1909. 

The  inclination  of  the  orbit  is  small,  —  1°  51 '. 

The  planet's  sidereal  period  is  687  days,  or  one  year  and  ten 
and  one-half  months ;  its  synodic  period  is  much  the  longest  in 
the  planetary  system,  being  780  days,  or  nearly  two  years  and 
two  months.  During  710  of  the  780  days  it  moves  eastward, 
and  during  70  retrogrades  through  an  arc  of  18°. 

408.  Magnitude,  Mass,  etc. —  The  apparent  diameter  of  the 
planet  ranges  from  3". 6  at  conjunction  to  24". 5  at  a  favorable 


362 


MANUAL   OF   ASTRONOMY 


Diameter, 
etc. 


opposition.  Its  real  diameter  is  very  near  4200  miles.  This 
makes  its  surface  about  two  sevenths,  and  its  volume  one  seventh, 
of  the  earth's. 

Its  mass  is  a  little  less  than  one  ninth  of  the  earth's  mass 
and  is  accurately  determined  by  means  of  its  satellites.  Its 
density  is  0.73,  as  compared  with  the  earth's,  and  its  superficial 
gravity  0.38 ;  a  body  which  here  weighs  100  pounds  would  have 
a  weight  of  only  38  pounds  on  the  surface  of  Mars. 

409.  General  Telescopic  Aspect,  Phases,  Albedo,  Atmosphere, 
etc. —  When  the  planet  is  nearest  the  earth  it  is  more  favorably 
situated1  for  telescopic  observation  than  any  other  heavenly 
body,  the  moon  alone  excepted.  It  then  shows  a  ruddy  disk 
which,  with  a  power  of  75,  is  as  large  as  the  moon.  Since  its 
orbit  is  outside  the  earth's,  it  never  exhibits  the  crescent  phases 
lik#  Mercury  and  Venus ;  but  at  quadrature  it  appears  distinctly 
gibbous,  about  like  the  moon  three  days  from  the  full. 

Like  Mercury,  Venus,  and  the  moon,  its  disk  is  brighter  at 
the  limb  (i.e.,  at  the  circular  edge)  than  at  the  center;  but  at 
the  terminator,  or  boundary  between  day  and  night  on  the 
planet's  surface,  there  is  a  shading  which,  taken  in  connection 
wdth  certain  other  phenomena,  indicates  the  presence  of  an 
atmosphere. 

This  atmosphere,  however,  contrary  to  opinions  formerly  held, 
is  probably  much  less  dense  than  that  of  the  earth,  the  low  den- 
sity being  indicated  by  the  infrequency  of  clouds  and  of  other 
atmospheric  phenomena  familiar  to  us  upon  the  earth,  to  say 
nothing  of  the  fact  that,  since  the  planet's  superficial  gravity  is 
less  than  two  fifths  of  the  force  of  gravity  on  the  earth,  a  dense 
atmosphere  would  be  impossible. 

More  than  twenty  years  ago  Huggins,  Janssen,  and  Vogel 
all  reported  the  lines  of  water  vapor  in  the  spectrum  of  the 
planet's  atmosphere ;  but  the  observations  of  Campbell,  at  the 

1  Venus  at  times  comes  nearer,  but  when  nearest  she  is  visible  only  by 
daylight,  and  shows  only  a  very  thin  crescent, 


THE   TERRESTRIAL   AND  MINOR   PLANETS  363 

Lick  Observatory  in  1894,  throw  great  doubt  on  their  result 
and  show  that  the  water  vapor,  if  present  at  all,  is  too  small  in 
amount  to  give  decisive  evidence  of  its  presence.1 

Zollner  gives  the  albedo  of  Mars  as  0.26,  —  just  double  that  Albedo  low. 
of  Mercury,  and  much  higher  than  that,.cf  the  moon,  but  only 
about  half  that  of  Venus  and  the  major  planets.     Near  opposi- 
tion the  brightness  of  the  planet  suddenly  increases  in  the  same 
way  as  that  of  the  moon  near  the  full  (Sec.  210). 

410.  Rotation,  etc.  —  The  spots  upon  the  planet's  disk  enable  notation 
us  to  determine  its  period  of  rotation  with  great  precision.     Its  Penodv(jry 
sidereal  day  is  found  to  be  24h37m22s.67,  with  a  probable  error  known, 
not  to  exceed  one  fiftieth  of  a  second.     This  very  exact  deter- 
mination is  effected  by  comparing  drawings  of  the  planet  made 

by  Huyghens  and  Hooke  more  than  two  hundred  years  ago  with 
others  made  recently. 

The  inclination  of  the  planet's  equator  to  the  plane  of  its  orbit  Position  of 
is,  according  to  Lowell's  latest  determination,  very  nearly  24°00'  axis' 
(25°30'  to  the  ecliptic).     So  far,  therefore,  as  depends  upon  that 
circumstance,  Mars  should  have  seasons  substantially  the  same 
as  our  own,  and  certain  phenomena  of  the  planet's  surface,  soon 
to  be  described,  make  it  evident  that  such  is  the  case. 

The  planet's  rotation  causes  a  slight  but  sensible  flattening  at  Obiate- 
the  poles,  —  about  ^l-^,  according  to  the  latest  determinations.     ness^5- 

411.  Surface  and  Topography. — With  even  a  small  telescope,  Surface 
not  more  than  3  or  4  inches  in  diameter,  the  planet  is  a  very  markmss 
beautiful  object,  showing  a  surface  diversified  with  markings 

dark  and  light,  which,  for  the  most  part,  are  found  to  be  perma- 
nent objects.  Occasionally,  however,  for  a  few  hours  at  a  time, 
we  see  others  of  a  temporary  character,  supposed  to  be  clouds, 
since  they  for  the  time  obliterate  the  permanent  ones ;  but  these 
are  surprisingly  rare  as  compared  with  clouds  upon  the  earth. 

-  *  A  similar  result  was  obtained  by  Campbell  in  1909,  when  the  observations 
were  repeated  under  favorable  conditions. 


364 


MANUAL   OF   ASTRONOMY 


The  permanent  markings  on  the  planet  are  broadly  divisible 
into  three  classes. 

First,  the  white  patches,  two  of  which  are  specially  conspicuous 
near  the  planet's  poles  and  are  called  the  "  polar  caps."  They 
are  by  many  supposed  to  be  masses  of  snow  or  ice,  since  they 
behave  just  as  would  be  expected  if  such  were  the  case.  The 
northern  one  dwindles  away  during  the  northern  summer,  when 
the  north  pole  is  turned  towards  the  sun,  while  the  southern  one 

grows  rapidly 
larger ;  and  vice 
versa  during  the 
southern  summer. 
But  the  prob- 
able low  temper- 
at ure  of  the 
planet  (Sec.  415) 
makes  it  at  least 
doubtful  whether 
the  apparent 
"  snow  and  ice  " 
is  really  con- 
gealed water,  or 
some  quite  differ- 
ent substance. 

Second,  patches  of  a  bluish  gray  or  greenish  shade,  covering 
about  three  eighths  of  the  planet's  surface,  until  recently  gener- 
ally supposed  to  be  bodies  of  water,  and  therefore  called  "  seas  " 
and  "  oceans."  But  more  recent  observations,  if  they  can  be 
depended  on,  show  a  great  variety  of  details  within  these  areas, 
and  such  changes  of  appearance  following  the  seasons  of  the 
planet,  that  this  theory  is  no  longer  tenable,  and  they  seem  more 
likely  to  be  regions  covered  with  something  like  vegetation. 

Third,  extensive  regions  of  various  shades  of  orange  and  yellow, 
covering  nearly  five  eighths  of  the  surface,  and  interpreted  as 


FIG.  141.  — Mars 

Keeler,  1892 


THE  TERRESTRIAL  AND  MINOR  PLANETS 


365 


land.     These  markings  are,  of  course,  best  seen  when  near  the  Continents, 
center  of  the  planet's  disk ;  near  the  limb  they  are  lost  in  the 
brilliant  light  which  there  prevails,  and  at  the  terminator  they 
fade  out  in  the  shade. 

Fig.  141 ,  from  drawings  by  Keeler  of  the  Lick  Observatory,  and  Fig.  142, 
from  drawings  by  Green  of  Madeira,  give  an  excellent  idea  of  the  planet's 
appearance  as  seen  by  most  observers  under  good  conditions. 

412.   Recent  Discoveries;  the  Canals  and  their  Gemination.— 
In  addition   to    these    three   classes  of   markings    the    Italian 
astronomer  Schiaparelli,  in  1877  and  1879,  reported  the  discov- 
ery of  a  great  number  of  fine  straight  lines, 
or  "  canals,"  as  he  called  them,  crossing  the 
ruddy  portions  of  the  planet's  disk  in  all 
directions,  and  in  1881  he  announced  that 
some  of  them  become  double  at  times. 

These  new  markings  are  faint  and  very 
difficult  to  see,  and  for  several  years  there 
was  a  strong  suspicion  that  he  was  misled  by 
some  illusion,  —  in  respect  to  their  "gemi- 
nation," at  least,  —  which  is  still  ascribed, 
by  some  very  high  authorities,  to  astigma- 
tism in  the  eye  of  the  observer  or  bad 
focusing  of  his  telescope.  Still,  the  weight 
of  evidence  at  present  favors  the  reality  of 
the  phenomena  which  Schiaparelli  describes. 
Many  observers,  both  in  Europe  and  the 
United  States,  have  confirmed  his  results, 
and  they  are  now  generally  accepted,  although  some  of  the  best, 
armed  with  very  powerful  telescopes,  still  fail  to  see  the  canals  C1JJ° ^Qs 
as  anything  but  the  merest  shadings.  It  appears  that  in  the  observe, 
observation  of  these  objects  the  power  of  the  telescope  is  less  Questlon  as 

J  to  possible 

important   than    steadiness    of   the   air   and    keenness   of   the  illusion^. 


FIG.  142 
Green,  1878 


366 


MAJSTUAL   OF   ASTRONOMY 


observer's  vision.  Nor  are  they  usually  best  seen  when  Mars  is 
nearest,  but  their  visibility  depends  largely  upon  the  season  of 
the  planet ;  and  this  is  especially  the  case  with  their  "  gemina- 
tion." Fig.  143,  from  one  of  Mr.  Lowell's  drawings  made  in 
1894,  gives  an  idea  of  the  extent  and  complexity  of  the  canal 
system;  but  the  reader  must  not  suppose  that  in  the  telescope 
it  stands  out  with  any  such  conspicuousness.  The  figure  shows 
also  how  some  of  the  canals  cross  the  so-called  useas"  and  dis- 
prove the  propriety  of  the  name. 

413.  As  to  the  real  nature  and  office  of  the  "  canals  "  there  is  a  wide 
difference  of  opinion,  and  it  is  very  doubtful  if  their  true  explanation 
has  yet  been  reached.  Indeed,  it  is  still  quite  probable  that  some  of  the 


FIG.  143.  — Mars 
After  Lowell 

peculiar  phenomena  reported  are  illusions,  based  on  what  the  observers 

think  they  ought  to  see  ;  it  is  easy  to  be  deceived  in  attempting  to  interpret 

intelligibly  what  is  barely  visible. 

Views  of  According  to  Flarnmarion,  Lowell,  and  other  zealous  observers  of  the 

Flammarion    planet,  the  polar  caps  are  really  snow  sheets,  which  melt  in  the  (Martian) 
and  Lowell,     spring  and  send  the  water  towards  the  planet's  equator  over  its  nearly  level 

plains  (for  no  high  mountains  have  yet  been  discovered  there),  obscuring 

for  several  weeks  the  well-known  markings  which  are  visible  at  other 

times. 

In  Lowell's  view  the  dark  regions  on  the  planet's  surface  are  areas 

covered  with  some  sort  of  vegetation,  while  the  ruddy  portions  are  barren 


THE   TERRESTRIAL   AND   MINOR   PLANETS 


367 


deserts,  intersected  by  the  canals,  which  he  believes  to  be  really  irrigating  Office  of 
watercourses ;  and  on  account  of  their  straightness,  and  some  other  charac-  tlie  canals, 
teristics,  he  is  disposed  to  regard  them  as  artificial. 

When  the  water  reaches  these  canals  vegetation  springs  up  along  their 
banks,  and  these  belts  of  verdure  are  what  we  see  with  our  telescopes,  — 
not  the  narrow  water  channels  themselves. 

Where  the  canals  cross  each  other  and  the  water  supply  is  more  abun-  Vegetation 
dant  there  are  dark  round  "  lakes,"  as  they  have  been  called,  which  he  and  oases, 
interprets  as  oases. 

All  of  this  theoretical  explana- 
tion rests,  however,  upon  the 
assumption  that  the  planet's  tem- 
perature is  high  enough  to  permit 
the  existence  of  water  in  the 
liquid  state,  to  say  nothing  of 
other  difficulties.  But  whatever 
may  be  the  explanation,  there  is 
no  longer  much  doubt  as  to  the 
existence  of  the  canals,  nor  that 
they  and  other  features  of  the  sur- 
face undergo  real  changes  with  the 
progress  of  the  planet's  seasons. 

Their  "gemination,"  however, 
still  remains  a  mystery,  nor  is  it 
entirely  certain  that  it  may  not  be 
a  purely  optical  effect,  as  already 
intimated;  experiments  made  at 
Harvard  College  Observatory  in 
1896,  and  later  in  France,  point 
strongly  in  this  direction. 

Certain  changes  on  the  surface 

of  the  planet  are  clearly  connected  with  its  seasons.     This  is,  of  course,    Seasonal 
the  case  with  the  alternate  growth  and  shrinkage  of  the  polar  caps,  and  changes. 
Flammarion  and  Lowell  have  reported  others.     Fig.  144,  from  the  obser- 
vations of  Lowell  in  1894,  shows  their  nature  and  amount. 

414,  Maps  of  the  Planet.  —  Numerous  maps  of  Mars  have  been  Maps  of 
constructed  by  various  observers.     Fig.  145   is  reduced  from  Mars* 
Schiaparelli's  map  of  1888,  and  shows  most  of  his  "canals" 
and  their  "  gemination."     While  the  accuracy  of  minor  details 
may  be  questionable,  the  leading  features  are  doubtless  correct. 


FIG.  144.  —  Seasonal  Changes  on  Mars 
Lowell 


368 


MANUAL   OF  ASTRONOMY 


THE   TERRESTRIAL  AND   MINOR   PLANETS  369 

The  nomenclature,  however,  is  in  a  very  unsettled  condition. 
Schiaparelli  has  taken  his  names  mostly  from  ancient  geography, 
while  the  English  areographers,1  following  the  analogy  of  the 
lunar  maps,  have  mainly  used  the  names  of  astronomers  who 
have  contributed  to  our  knowledge  of  the  planet's  surface. 

In  1905  photographs  showing  clearly  the  principal  features  of  Photographs, 
the  planet  were  obtained  (by  Lampland)  at  Lowell's  Flagstaff 
Observatory,  —  a  great  advance. 

415.  Temperature. — As  to  the  temperature  of  Mars  we  have  Temper- 
no  certain  knowledge  at  present.     Unless  the  planet  has  some  a*ure  of  the 
unexplained  sources  of  heat  it  ought  to  be  very  cold.  a  priori, 

Its  distance  from  the  sun  reduces  the  intensity  of  solar  radia-  supposably 

low 

tion  upon  its  surface  to  less  than  half  its  value  upon  the  earth,2 
and  its  atmosphere  cannot  well  be  as  dense  as  at  the  tops  of  our 
loftiest  mountains. 

On  the  other  hand,  things  look  very  much  as  if  the  poles 
were  really  snow-capped,  and  as  if  liquid  water  and  vegetable 
life  were  present  in  other  regions. 

If  so,  we  must  suppose  that  the  planet  has  sources  of  heat,  Facts  that 
external  or  internal,  which  are  not  yet  explained;  otherwise  the  su^est 

unknown 

polar  "snow"  must  be  something  else  than  frozen  water,  as  is  sources 
perhaps  not  impossible.     It  is  earnestly  to  be  hoped,  and  may  be  of  heat- 
expected,  that  before  long  we  shall  obtain  some  heat-measuring 
apparatus  sufficiently  delicate  to  decide  whether  the  planet's 
surface   is  really  intensely  cold  or  reasonably  warm,  —  for  of 
course  there  are  various  conceivable  hypotheses  which  might 
explain  a  high  temperature  at  the  surface  of  Mars. 

416.  Satellites.  —  The  planet  has  two  satellites,  discovered  Satellites: 
by  Hall,  at  Washington,  in  1877.     They  are  extremely  small 

and  observable  only  with  very  large  telescopes.    The  outer  one,  names. 
Deimos,  is  at  a  distance  of  14600  miles  from  the  planet's  center 
and  has  a  sidereal  period  of  30h18m;  while  the  inner  one,  Phobos, 

1  The  Greek  name  of  Mars  is  Ares ;  hence,  areography  is  the  description  of 
the  surface  of  Mars. 

8  See  Addendum  B,  at  beginning  of  book.    . 


370 


MANUAL   OF   ASTRONOMY 


Suggestion  of 
intelligence 
in  the  system 
of  canals. 


is  at  a  distance  of  only  5800  miles  and  has  a  period  of  7h39m,— 
less  than  one  third  of  the  planet's  day.  (This  is  the  only  case 
known  of  a  satellite  with  a  period  shorter  than  the  revolution 
of  its  primary.)  Owing  to  this  fact,  it  rises  in  the  west,  as  seen 
from  the  planet's  surface,  and  sets  in  the  east,  completing  its 
strange  backward  diurnal  revolution  in  about  eleven  hours. 
Deimos,  on  the  other  hand,  rises  in  the  east,  but  takes  nearly 
132  hours  in  its  diurnal  circuit,  which  is  more  than  four  of  its 
months.  Both  the  orbits  are  sensibly  circular  and  lie  very 
closely  in  the  plane  of  the  planet's  equator. 

Micrometric  measures  of  the  diameter  of  such  small  objects 
are  impossible,  but,  from  photometric  observations,  Prof.  E.  C. 
Pickering,  assuming  that  they  have  the  same  reflecting  power 
as  that  of  Mars  itself,  has  estimated  the  diameter  of  Phobos  as 
about  7  miles  and  that  of  Deimos  as  5  or  6.  Mr.  Lowell,  how- 
ever, from  his  observations  of  1894,  deduces  considerably  larger 
values,  viz.,  10  miles  for  Deimos  and  36  for  Phobos.  If  this  is 
correct,  Phobos,  seen  in  the  zenith  from  the  point  on  the  planet's 
surface  directly  beneath  him,  would  appear  somewhat  larger  than 
the  moon,  but  only  about  half  as  bright.  Deimos  when  "  full " 
would  be  perhaps  considerably  brighter  than  Venus. 

417.  Habitability  of  Mars.  —  As  to  this  question  we  can  only 
say  that,  different  as  must  be  the  conditions  on  Mars  from  those 
prevailing  on  the  earth,  they  differ  less  from  ours  than  those  on 
any  other  heavenly  body  observable  with  our  present  telescopes; 
and  if  life,  such  as  we  know  it  upon  the  earth,  can  exist  on  any 
of  the  planets,  Mars  is  the  one.  If  we  could  waive  the  ques- 
tion of  temperature  and  assume,  with  Flammarion  and  others, 
that  the  polar  caps  really  consist  of  frozen  water,  then  it  would 
become  extremely  probable  that  the  growth  of  vegetation  is  the 
explanation  of  many  of  the  phenomena  actually  observed. 

Mr.  Lowell  goes  further  and  argues  the  presence  of  intelligent 
beings,  possessed  of  high  engineering  skill,  from  the  apparent 
"  accuracy  "  with  which  the  "  canals  "  seem  to  be  laid  out  in  a 


THE   TERRESTRIAL   AND  MINOR  PLANETS  371 

well-planned  system  of  irrigation.  But  at  present,  and  until 
the  temperature  problem  is  solved,  such  speculations  appear 
rather  premature;  and  as  to  the  establishment  of  communica- 
tion with  the  hypothetical  inhabitants,  the  idea,  in  the  present 
state  of  human  arts  at  least,  is  simply  chimerical. 

THE  ASTEEOIDS 

418.  The  "  asteroids,"  or  minor  planets,  are  a  host  of  small 
bodies  circulating,  with  few  exceptions,  between  the  orbits  of 
Mars  and  Jupiter.  The  name  "asteroid,"  i.e.,  "  starlike,"  was 
suggested  by  Sir  William  Herschel  early  in  the  century,  as 
indicating  that,  though  really  planets,  they  appear  like  stars. 

Kepler  had  noticed  the  wide  gap  between  Mars  and  Jupiter  The  aster- 
and  had  tried  to  account  for  it,  though  unsuccessfully,  and  Oldstaking 
when  Bode's  Law  (Sec.  349)  was  published  in  1772  the  impres-  Of  a  single 
sion  became  very  strong  that  there  must  be  a  missing  planet  in  pianet  in 
the  vacant  space,  —  an  impression  greatly  strengthened  by  the  cated  by 
discovery  of  Uranus  in  1781,  at  a  distance  almost  precisely  Bode's  Law. 
corresponding    to    that   law.      An    association   of   twenty-four 
astronomers,  mostly  German,  was  formed  to  look  for  the  miss- 
ing planet,  but  failed  to  find  one  after  a  dozen  years  of  search, 
and  the  first  discovery  was  made  by  the  Sicilian  astronomer, 
Piazzi,  who  was  then  engaged  in  forming  his  extensive  cata- 
logue of  stars. 

On  the  first  night  of  the  nineteenth  century  (Jan.  1,  1801)  Discovery 
he  observed  a  small  star  where  there  had  been  no  star  a  few  of  Ceres  by 

Piazzi. 

days  earlier,  and  the  next  day  it  had  obviously  moved,  and  it 
continued  to  move.  He  named  the  new  planet  Ceres,  after  the 
tutelary  divinity  of  the  island,  and  observed  it  carefully  for 
several  weeks,  until  he  was  taken  ill;  but  before  he  recovered 
the  planet  was  lost  in  the  evening  twilight.  It  was  redis- 
covered at  the  close  of  the  next  year  by  means  of  Gauss' 
calculations.  (See  Sec.  365.) 


372 


MANUAL   OF   ASTRONOMY 


Discovery 
of  Pallas, 
Juno,  and 
Vesta. 


Discovery 
of  Astraea. 


Over  seven 

hundred 

known. 

Designation 
by  numbers 
and  names. 


Method  of 
search  with 
telescope. 


Photo- 
graphic 
method. 


In  1802,  while  searching  for  Ceres,  Pallas  was  discovered  by 
Olbers.  Juno  was  found  by  Harding  in  1804,  and  in  1807 
Olbers,  who  had  broached  the  theory  that  these  new  bodies 
were  fragments  of  an  exploded  planet,  discovered  Yesta,  the 
only  one  ever  visible  to  the  naked  eye.  The  search  was  kept  up 
for  several  years  longer  without  success,  because  those  engaged 
in  it  did  not  look  for  small  enough  objects. 

The  fifth  asteroid,  Astrcea,  was  discovered  in  1845  by  Hencke, 
an  amateur,  who  had  resumed  the  search  afresh  by  studying 
the  smaller  stars  and  after  fifteen  years  of  fruitless  labor  was 
rewarded  by  the  new  discovery.  In  1847  three  more  were  found, 
and  not  a  year  has  passed  since  then  without  the  discovery  of 
from  one  to  thirty. 

Already  the  number  catalogued  exceeds  seven  hundred  and 
since  1891  has  been  increasing  with  great  rapidity.  Most  of 
those  recently  discovered  are  below  the  twelfth  magnitude. 

They  are  all  designated  by  numbers ;  i.e.,  each  one  receives 
a  number  after  having  been  observed  a  sufficient  number  of 
times  to  determine  its  orbit,  —  which  usually  happens  soon  after 
its  discovery.  Most  of  them  also  have  names,  usually  mytho- 
logical, and  feminine  for  all  but  Eros  and  the  "  Jupiter  group,"  1 
but  it  is  no  longer  easy  to  find  names  for  all  the  new  discoveries, 
and  many  of  the  recent  ones  have  none. 

419.  Method  of  Search. — Formerly  the  asteroid  hunter  con- 
ducted his  operations  by  making  special  telescopic  star  charts 
of  regions  near  the  ecliptic,  and  from  time  to  time  comparing 
the  chart  with  the  heavens.  If  an  interloper  appeared  on  the 
chart,  a  few  hours'  watching  would  decide  whether  it  moved  or 
not,  i.e.,  whether  it  was  a  planet  or  merely  a  variable  star.  The 
work,  especially  that  of  chart  making,  was  very  laborious. 

In  1891  a  new  method  was  introduced  by  Dr.  Max  Wolf  of 

Heidelberg.     A  camera  with  a  wide-angle  lens  of  several  inches 

aperture    is  mounted  equatorially  and   moved  by  clockwork; 

with  this  photographs  are  made  of  portions  of  the  sky  from  5° 

1  See  Addendum  C,  at  beginning  of  book. 


THE   TERRESTRIAL   AND   MINOR   PLANETS 


373 


to  10°  in  diameter.  On  the  negative  the  stars,  if  the  clock- 
work runs  correctly,  show  as  small  black  dots,  but  a  planet,  if 
present,  will  move  among  the  stars  during  the  two  or  three 
hours  of  exposure,  and  its  image  will  be  a  streak  instead  of  a 
dot,  and  so  recognizable  at  once. 

Fig.  146  is  a  direct  reproduction  of  the  plate  on  which  Dr.  Wolf  dis- 
covered planet  1892,  V  (Gudrun,  (328)  ),  the  "  trail  "  of  which,  due  to  about 
two  hours  motion,  is  shown  exactly  in  the  center  of  the  cut.     The  first 
planet  discovered  by  this  method,  in  December,  1891,  Wolf  has  named 
"Brucia,"  (323),   in  honor  of 
the  late  Miss   Catherine  W. 
Bruce  of  New  York,  who  pro- 
vided the  funds  for  his  camera 
and  its  mounting. 

It  has  happened  several 
times  that  more  than  one 
planet  is  found  on  the 
negative ;  in  one  instance 
as  many  as  five,  three  of 
which  were  new,  and  in 
another  (on  a  plate  made 
at  Harvard)  no  less  than 
seven.  Already,  during 
the  past  ten  years,  nearly 
three  hundred  have  been  thus  discovered,  almost  all  by  Wolf  of 
Heidelberg  and  Charlois  of  Nice,  though  a  few  others  have 
contributed.1 

Great  care  is  necessary  to  be  sure  that  the  objects  discovered  are  really 
new.  There  are  a  number  of  the  older  ones  which,  not  having  been  observed 
for  many  years,  are  now  adrift  and  practically  lost,  and  are  likely  to  be 
rediscovered  at  any  time.  Several  of  them  indeed  have  been  already 
picked  up  by  the  new  method.  Provisional 

Since  1892  the  newly  discovered  bodies,  while  awaiting  the  final  num-  designation 
bers  (and  perhaps  a  name),  are  provisionally  designated  by  letters,  as  AM,    assignment 

etc.  of  number. 

1  See  Addendum  C,  at  beginning  of  book. 


FIG.  146.  —  Wolf's  Discovery  of 
"Gudrun,"  1892 


374  MANUAL   OF   ASTRONOMY 

A  full  list,  brought  down  to  date  as  nearly  as  possible,  is  published 
biennally  in  the  Annuaire  du  Bureau  des  Longitudes,  Paris,  giving  their 
number,  name,  date  of  discovery,  and  the  elements  of  their  orbits. 


THEIR   ORBITS 

Distance  420.    Mean  Distance  and  Period.  —  The  mean  distances  of  the 

and  period:    different  asteroids  from  the  sun  differ  widely,  and  their  periods 

Adalberta 

nearest,  correspond.  Excepting  Eros,  the  nearest  to  the  sun  so  far  as 
Thuie  yet  determined  is  Hungaria,  (434),  its  mean  distance  being  about 

Mods8 '  1'94  (180  800000  miles)  and  its  period  two  years  and  nine 
three  to  nine  months.  Thule,  (279),  is  the  most  remote,1  with  a  distance  of 
years.  4  g^  or  ^QQ  QOOOOO  miles,  and  a  period  only  a  month  less  than 

nine  years. 

The  mean  distances   are    not   distributed   at  all    uniformly 
through  their  range,  but  there  are  several  marked  gaps,  doubt- 
less due  to  the  action  of  Jupiter,  since  they  come  just  where 
Average        the  period  of  the   asteroid  would  be   exactly  commensurable 
mean  dis-      with  foot,  of  the  great  planet,  i.e.,  £,  i-,  £,  or  I  of  Jupiter's 

tance  of  °      ^      ° 

group  about   period.     The  distances   are  grouped  most  densely  about  2.8, 

2.65.  which  Bode's  Law  would  indicate  as  that  of  the  "  missing " 

planet;   but  the  average  mean  distance  comes  out  somewhat 

smaller,   about    2.65    (246  500000  miles),    corresponding   to    a 

period  of  about  four  and  one- third  years. 

Large  incii-  421.  Inclinations  and  Eccentricities.  —  These  average  much 
nationsand  ~reater  ^han  for  the  principal  planets.  The  mean  inclina- 

eccentrici- 

ties.  tion  of  the  asteroid  orbits  to  the  ecliptic  is  about  8°.     The 

orbit  of  Pallas,  (2),  is  inclined  35°,  and  seven  or  eight  others 
exceed  25°. 

The  eccentricity  is  also  very  large  in  some  cases.  For 
JEthra,1  (132),  and  Andromache,  (175),  it  is  fairly  cometary, 
exceeding  0.35,  and  there  are  a  dozen  others  above  0.30. 

1  See  Addendum  C,  at  beginning  of  book. 


THE   TERRESTRIAL  AND   MINOR   PLANETS  375 

The  orbits  so  cross  and  interlink  that  if  they  were  material 
hoops  or  rings  the  lifting  of  one  would  take  all  the  others  with 
it,  and  that  of  Mars  also,  caught  up  by  that  of  Eros. 

422.  Diameter,  Surface,  etc These  bodies  are  so  small  that  Diameters 

micrometrical  measurements,  even  of  the  largest,  are  extremely  for  most 
difficult,    and   of  the   smaller   ones    impossible.      Since    1890,   small  for 
however,  Barnard,  with  the  Lick  and  Yerkes  telescopes,  has  measure- 
obtained  measures  of  the  disks  of  the  four  brightest  and  presum- 
ably largest,  with  the  following  rather  surprising  results,  viz. : 

Ceres,  488  miles;  Pallas,  304;  Vesta,  248;  Juno,  118.     The  Barnard's 
surprise  consists  in  the  fact  that  Vesta,  which  is  fully  twice  as  results  for 

CJpros 

bright  as   Ceres,  should  have   a  diameter  only  half  as  great,  paiia^ 
showing   a  wide   difference    of   albedo.      Miiller  of   Potsdam,  Vesta,  and 
accepting  Barnard's  diameters,  finds  for  Ceres  from  his  photo- 
metric observations  an  albedo  about  the  same  as  that  of  Mercury 
(0.13),  while  that  of  Vesta  is  put  at  0.72,  — higher  than  that  of 
any  other  planet,  and  nearly  equal  to  that  of  writing-paper. 

As  to  the  other  asteroids,  probably  no  one  of  them  has  a 
diameter  as  great  as  100  miles,  and  the  smaller  ones,  such  as 
those  which  are  now  being  discovered,  are  mostly  of  the  thir- 
teenth and  fourteenth  magnitude,  so  small  that  they  cannot  be 
seen  (though  easily  photographed)  with  a  telescope  of  much  less 
than  12  inches  aperture  and  cannot  be  more  than  10  or  15  miles 
in  diameter,  —  mere  "mountains  broke  loose,"  with  a  surface 
area  no  more  extensive  than  some  western  farms. 

423.  Mass  and  Density.  —  On  these  points  we  have  no  abso-  Mass  of 
lute  knowledge ;  but  if  we  assume  that  the  density  is  about  the  Ceres  pxer" 
same  as  that  of  the  planet  Mars  (seventy-three  per  cent  of  the  earth's, 
density  of  the  earth),  which  is  probably  an  overestimate,  Ceres 
would  have  a  mass  of  about  -^ViT  tnat  °^  tne  eartn>  an(*  the  force 

of  gravity  at  her  surface  would  be  about  -fa  of  gravity  here. 

A  stone  would  descend  only  about  8£  inches  in  the  first  second  of  its   Force  of 
fall,  and  the  "  parabolic  velocity  "  at  the  planet's  surface  would  be  about   £ravity  on 
1900  feet  a  second  (Sec.  319),  — a  rifle  bullet  shot  from  the  planet  would   asteroids- 


376 


MANUAL   OF   ASTRONOMY 


Total  mass 
of  group 
certainly 
less  than 
a  of  earth's, 
perhaps  less 
than  i Jo. 


Total 
number 
probably 
thousands. 


Theories  as 
to  origin. 


never  return.  For  a  planet  10  miles  in  diameter  of  the  same  density,  the 
critical  velocity  would  be  only  38  feet  a  second,  so  that  if  the  hypothetical 
dweller  on  one  of  these  "  planetules,"  as  Miss  Clerke  calls  them,  should 
throw  away  a  stone,  it  would  never  come  back,  but  would  become  an  inde- 
pendent planet. 

It  is,  however,  possible  from  the  perturbations  which  the 
asteroids  produce  (or  rather  do  not  produce)  on  Mars  to  esti- 
mate, for  the  aggregate  mass  of  the  flock,  a  limit  which  it 
cannot  exceed,  —  including  the  presumably  undiscovered  multi- 
tude as  well  as  the  five  hundred  now  known.  Leverrier  found 
long  ago  that  the  total  mass  could  not  be  as  great  as  one  quarter 
the  mass  of  the  earth ;  and  a  much  more  recent  computation  by 
Raveiie  in  189G  puts  it  below  one  per  cent.  The  united  mass 
of  all  thus  far  discovered  would  make  but  a  small  fraction  of 
this  one  per  cent,  —  certainly  not  over  I-$-$-Q  of  the  mass  of  the 
earth. 

424,  The  number  not  yet  discovered  is  probably  enormous, 
though  it  is  practically  certain  that  nearly  all  that  exceed  40  or 
50  miles  in  diameter  are  already  in  our  catalogue.     How  long 
it  will  be   considered  worth  while   to  search  for  new  ones  is 
doubtful,  as   it  is   quite  certain  that  the   computers   will  not 
continue  to  follow  by  calculation   the  motions  of  any  except 
such  as  possess  peculiar  interest  for  their  size  or  some  other 
reason. 

An  asteroid  is  much  more  difficult  to  observe  than  a  large  planet,  and 
immensely  more  troublesome  to  follow  by  calculation,  because  of  the  great 
perturbations  to  which  it  is  exposed  from  Jupiter's  attraction.  One  little 
family  of  these  bodies,  twenty-two  in  number,  which  were  discovered  by 
Professor  Watson  of  Ann  Arbor,  is,  however,  "  endowed "  with  a  fund 
which  he  left  in  his  will  to  pay  for  the  calculations  necessary  to  keep  them 
from  getting  lost. 

425.  Origin.  —  As  to  this  we  can  only  speculate.     It  is  hardly 
possible  to  doubt  that  this  swarm  of  little  rocks  in  some  way 
represents  a  single  planet  of  the  terrestrial  group. 


THE   TERRESTRIAL   AND   MINOR   PLANETS  377 

A  generally  accepted  view  is  that  the  material,  which,  accord- 
ing to  the  nebular  hypothesis,  once  formed  a  ring  or  rings  like 
those  of  Saturn,  either  continuous  or  of  separate  pieces, — matter 
which  ought  to  have  collected  to  make  a  single  planet,  —  has  Aringdis- 
failed  to  be  so  concentrated;  and  the  failure  is  ascribed  to  the  ruPtedby 

attraction  of 

perturbations  produced  by  its  neighbor,  the  giant  Jupiter,  whose  Jupiter, 
powerful  attraction  is  supposed  to  have  disintegrated  the  ring, 
or  at  least  prevented  the  union  of  the  separate  parts,  and  thus 
stopped  the  development  of  a  normal  planet. 

Another  view  is  that  the  asteroids  may  be  fragments  of  an  ATI  exploded 
exploded  planet.     If  so,  there  must  have  been  not  one  but  many  i)lanet- 
explosions :   first  of  the  original,  and  then  of  the  separate  pieces 
in  different  portions  of  their  orbits.     It  is  demonstrable  that  no 
single  explosion  could  account  for  the  present  tangle  of  orbits. 

426.  The  Planet  Eros.  —  This  little  planet,  insignificant  in  Eros  a 
size  but  of  great  astronomical  interest,  and  already  several  times  doubt£ul 
referred  to,  should  probably  be  regarded  as  a  member  of  the  the  asteroid 
asteroid  family.    It  has,  however,  an  orbit  so  much  smaller  than  family, 
any  other  asteroid  that  the  discoverer  claims  for  it  a  status  of 

its  own. 

It  was  discovered  in  August,  1898,  photographically,  by  Witt  its  dis- 
of  Berlin,  and  at  once  attracted  notice  by  the  rapidity  of  its  c>overy 
motion.     After  a  preliminary  calculation  of  its  orbit  had  been 
made  by  Dr.  Chandler,  so  that  its  place  could  be  approximately 
computed  for  dates  in  the  past,  its  trail  was  found  on  a  con- 
siderable number  of  photographic  plates  made  at  Harvard  Col- 
lege Observatory  during  several  years  preceding  (1893,  1894, 
and  1896);  and  this  rendered  it  possible  at  once  to  compute 
a  very  accurate  orbit. 

427,  Orbit  of  Eros.  —  Its  mean  distance  from  the  sun  is  only  its  orbital 
1.46  (135  500000  miles).     Its  sidereal  period  is  643  days,  its  £eecsuliari~ 
synodic  845  days.     The  eccentricity  of  its  orbit  is  0.22,  which 

makes  the  aphelion  distance  165  500000  miles  (well  outside  the 
orbit  of  Mars  and  well  within  the  asteroid  region),  while  its 


378 


MANUAL   OF   ASTRONOMY 


Its  occa- 
sional close 
approach  to 
the  earth. 
Important 
as  a  means 
of  determin- 
ing solar 
parallax. 


Next  oppor- 
tunity in 
1931. 


Enormous 
range  of 
brightness 


Periodic 
variations  of 
brightness. 


perihelion  distance  (105  300000  miles)  is  only  a  little  more 
than  12  000000  miles  greater  than  the  mean  distance  of  the 
earth  from  the  sun.  Its  orbit  is  shown  in  Fig.  125. 

The  inclination  of  its  orbit  is  11°,  and  this,  combined  with 
the  fact  that  the  perihelion  of  the  planet's  orbit  nearly  faces 
that  of  the  earth,  makes  the  least  possible  distance  between  the 
earth  and  Eros  about  13  500000  miles.  This  is  only  a  little 
more  than  half  the  least  distance  of  Venus,  and  it  gives  the 
planet  immense  importance  from  an  astronomical  point  of  view, 
since  observations  made  at  such  a  time  of  close  approach  will 
furnish  a  far  more  precise  determination  of  the  solar  parallax 
and  astronomical  unit  than  any  other  method  known. 

Unfortunately,  these  close  oppositions  are  rare ;  one  occurred 
in  1894,  and  another  such  opportunity  will  not  occur  again 
until  1931.  In  the  winter  of  1900-01  the  conditions  were 
better  than  they  will  be  until  then,  the  planet  having  come 
within  about  30  000000  miles  of  the  earth.  An  extensive  series 
of  observations,  both  visual  and  photographic,  was  made,  par- 
ticipated in  by  all  the  leading  observatories  of  the  world.  The 
mass  of  material  accumulated  is  such  that  it  will  probably  be 
several  years  before  the  results  can  be  fully  worked  out.1 

428.  Eros  itself.  —  The  planet  is  small,  probably  not  more 
than  15  or  20  miles  in  diameter,  though  this  is  merely  an  esti- 
mate. On  account  of  the  enormous  variation  in  its  distance 
from  the  earth  (from  13  500000  miles  to  260  000000),  its  bright- 
ness when  nearest  us  is  nearly  four  hundred  times  as  great  as 
when  remotest.  Near  aphelion  it  is  observed,  if  at  all,  only 
with  the  very  largest  telescopes ;  when  nearest,  in  1931,  it  will 
for  a  few  days,  perhaps,  become  visible  even  to  the  naked  eye. 

A  very  remarkable  thing  is  the  apparent  periodic  variation  in 
its  brightness  observed  during  the  early  winter  and  spring  of 
1901,  —  shown  also  in  some  of  the  Harvard  photographs  of 
1894  and  1896.  At  certain  times  the  variation  was  very 

1  In  1909  Professor  Hinks  of  Cambridge  (England)  announced  as  the  final  result 
from  measures  of  photographs,  8".806  ±  0".0027;  from  micrometer  measures, 
8".802  ±  0".0036. 


THE   TERRESTRIAL   AND  MINOR   PLANETS  379 

striking,  the  planet  in  February  and  March,  1901,  being  at  the 
maximum  fully  three  times  as  bright  as  at  the  minimum,  only 
two  and  one-half  hours  later.  At  other  times  the  variation 
disappeared  entirely,  as  in  May,  1901.  The  period  of  varia- 
tion, which  is  5h16m,  gives  some  evidence  of  two  unequal  half 
periods,  one  of  2h25m  and  the  other  of  2h51m,  but  this  is  not 
yet  certain. 

The  most  natural  explanation  of  the  variation,  as  already  mentioned   Explained 
(Sec.  383),  is  that  it  is  caused  by  the  axial  rotation  of  the  planet,  which  is   bF  rotation 
supposed  to  have  light  and  dark  markings  on  its  surface.     If  these  are   °  * s 
arranged  something  like  the  continents   on  the   earth  (continents  light,    the  revo_ 
oceans  dark),  the  variation  of  light  would  be  about  as  observed  when  we   lution  of 
are  in  the  plane  of  the  planet's  equator,  and  would  cease  when  the  planet's   tw°  bodies 
pole  is  directed  towards  us. 

Another  explanation,  preferred  by  the  French  astronomer  Andre",  is  that   form 
the  planet  is  double,  "  a  pair  of  twins,"  consisting  of  two  bodies  revolving   around 
around  each  other  almost  in  contact,  in  an  oval  orbit,  and  with  a  period  of   each  other. 
5h16m.     When  we  are  in  the  plane  of  the  orbit  occultations  occur  twice  in 
every  revolution,  one  of  the  bodies  eclipsing  the  other ;  but  on  account  of 
the  eccentricity  of  the  orbit  these  eclipses  are  not  at  equal  intervals. 

To  account  for  the  greatness  of  the  light  change  Andr6  further  supposes 
that  the  bodies  are  egg-shaped,  on  account  of  their  mutual  tidal  action,  so 
that  when  seen  sidewise  they  present  three  times  as  much  surface  as  when 
seen  "  end  on,"  one  behind  the  other.  It  remains  to  be  seen  what  future 
observations  may  show  as  to  the  rival  theories.  Similar  periodic  variability, 
less  marked  however,  has  since  been  detected  in  Sirona  (116),  Hertha 
(135),  and  Tercidina  (345).  Several  others  are  suspected. 

429.   Intramercurial  Planets. —  It  is  not  impossible  that  there  Possible 
is  a  considerable  quantity  of  matter  circulating  around  the  sun  mtramer- 
inside  the  orbit  of  Mercury.     This  has  been  believed  to  be  indi-  pianets. 
cated  by  the  otherwise  unexplained  advance  of  the  perihelion 
of  Mercury's  orbit,  but  the  investigations  of  Newcomb  render 
very  doubtful  the  validity  of  such  an  explanation,  since  the 
nodes  of  the  planet's  orbit  are  not  affected  as  they  would  be  on 
that  hypothesis.     It  has  been  somewhat  persistently  supposed 
that  this  intramercurial   matter  is  concentrated  into  one,   or 


380 


MANUAL   OF   ASTRONOMY 


Reported 
discovery 
of  Vulcan 
never 
verified. 


possibly  two,  planets  of  considerable  size,  and  such  a  planet 
has  several  times  been  reported  as  discovered,  notably  in  1857 
(when  it  was  even  named  "  Vulcan"),  and  again  in  1878.  We 
can  only  say  that  the  supposed  discoveries  have  never  been  con- 
firmed, and  the  careful  observations  during  total  solar  eclipses 
during  the  past  twenty  years  make  it  practically  certain  that 
there  is  no  "  Vulcan,"  i.e.,  no  single  considerable  planet.  Per- 
haps, however,  there  may  be  an  intramercurial  family  of  aster- 
oids. If  so,  they  must  be  verjr  small  or  some  of  them  would 
certainly  have  been  found  during  the  eclipses ;  and,  if  as  large 
as  100  or  200  miles  in  diameter,  some  of  them  would  probably 
have  been  caught  crossing  the  sun's  disk. 


Attempts  to          An  attempt  was  made  to  detect  any  existing  body  of  this  kind  during 
find  intra-       the  eclipses  of  1900  and  1901  by  means  of  photography.    Photographs  of 
extensive  areas  near  the  sun,  made  in  1905  and  1908,  make  it  practically 


mercurial 
planets  by 


photography    certain  tnat  there  are  no  intramercurial  bodies  brighter  than  the  eighth 
during  solar    magnitude. 


light:  its 
appearance 
and  when 
best  seen. 


430.  The  Zodiacal  Light.  —  This  is  a  faint  pyramid  of  light, 
for  the  most  part  less  luminous  than  the  Milky  Way,  extending 
The  zodiacal  from  the  sun  both  east  and  west  along  the  ecliptic.  In  northern 
latitudes  it  is  best  seen  in  the  evening  during  the  months  of 
February  and  March ;  in  the  morning,  in  October  and  November. 
Its  summit  is  sometimes  as  far  as  90°  from  the  sun,  and  in  the 
tropics  it  is  said  to  be  sometimes  visible  at  midnight  as  a  com- 
plete belt  extending  clear  across  the  heavens. 

Opposite  to  the  sun  there  is  a  slightly  brighter  patch  10° 
or  20°  in  diameter,  called  the  "Gegenschein,"  or  "counter 
glow."  This,  and  indeed  the  whole  phenomenon,  is  so  faint 
that  it  can  be  well  seen  only  when  the  observer  is  where  there 
is  no  interference  from  artificial  lights.  Even  the  presence  of 
one  of  the  brighter  planets  greatly  embarrasses  the  observation. 
The  region  near  the  sun  is  fairly  bright,  it  is  true,  but  is  always 
more  or  less  immersed  in  the  twilight. 


The  Gegen- 
schein. 


THE   TERRESTRIAL   AND   MINOR   PLANETS  381 

The  spectrum  is  a  simple  continuous  one,  without  perceptible  The  spec- 
lines  or  marking  of  any  kind.     We  emphasize  this  because  it  trum  of  the 

r  zodiacal 

has  often  been  erroneously  reported  that  it  shows  the  bright  light, 
yellow  line  which  characterizes   the    spectrum   of  the  aurora 
borealis. 

The  most  probable  explanation  of  the  zodiacal  light  is  that  Probable 
it  is  due  to  reflection  of  sunlight  from  myriads  of  small  particles  e^PJ^natlou 
revolving  around  the  sun  in  a  comparatively  thin,  flat  sheet  or  zodiacal 
ring  (something  like  Saturn's  ring),  which  extends  far  beyond  hshtasa 

J  meteoric 

the  orbit  of  the  earth,  and  perhaps  even  to  that  of  Mars.  ring. 

Near  the  sun  the  particles  are  supposed  to  be  more  numerous 
than  elsewhere,  as  well  as  more  brilliantly  illuminated,  so  that 
although  less  than  half  the  sunlit  surface  of  each  is  visible  to 
us,  yet  on  the  whole  the  total  sum  of  brightness  is  greater  than 
elsewhere.  As  for  the  Gegenschein,  this  may  be  accounted  for 
by  supposing  that  the  particles  nearly  opposite  the  sun  "  flash 
out "  in  the  same  way  that  the  moon  does  at  the  full. 

It  has  been  attempted  to  explain  the  zodiacal  light  as  due  to  a  ring  of 
meteoric  particles  revolving  around  the  earth  ;  but  in  that  case  the  Gegen- 
schein would  be  replaced  by  a  dark  spot  caused  by  the  shadow  of  the  earth. 


CHAPTER   XIV 
THE   MAJOR  PLANETS 

Jupiter :  its  Satellite  System ;  the  Equation  of  Light,  and  the  Distance  of  the  Sun  — 
Saturn:  its  Rings  and  Satellites  —  Uranus:  its  Discovery,  Peculiarities,  and 
Satellites  —  Neptune:  its  Discovery,  Peculiarities,  and  Satellite 


Orbital 
data. 


JUPITER 

Jupiter:  JUPITER,  the  nearest  of  the  major  planets,  stands  next  to 

its  conspicu-  yenus  in  the  order  of  brilliance  among  the  heavenly  bodies, 
being  five  or  six  times  as  bright  as  Sirius,  the  most  brilliant  of 
the  stars,  and  decidedly  superior  to  Mars,  even  when  Mars  is 
nearest.  It  is  not,  like  Venus,  confined  to  the  twilight  sky, 
but  at  the  time  of  opposition  dominates  the  heavens  all  night 
long. 

431.  Its  orbit  presents  no  marked  peculiarities.  The  mean 
distance  of  the  planet  from  the  sun  is  a  little  more  than  five 
astronomical  units  (483  000000  miles),  and  the  eccentricity  of 
the  orbit  is  not  quite  ^,  so  that  the  distance  from  the  sun  varies 
about  42  000000  miles  between  perihelion  and  aphelion. 

At  an  average  opposition  the  planet's  distance  from  the  earth 
is  about  390  000000  miles,  while  at  conjunction  it  is  about 
580  000000 ;  but  it  may  come  as  near  to  us  as  370  000000  and 
may  recede  to  a  distance  of  nearly  600  000000. 

The  sidereal  period  is  11.86  years,  and  the  synodic  period  is 
399  days  (a  figure  easily  remembered),  a  little  more  than  a  year 
and  a  month. 

Diameter,          432.    Diameter,  Mass,  Density,  etc.  —  The  planet's  apparent 
obiateness,     Diameter  ranges  from  50"  to  32",  according  to  its  distance  from 

surface,  and  &  & 

bulk.  the  earth.     The  disk,  however,  is  distinctly  oval,  the  equatorial 


THE   MAJOR   PLANETS  383 

diameter  being  nearly  90000  miles,  while  the  polar  diameter  is 


84200.     The  mean  diameter  (see  Sec.  139)  is  88000 

\  ' 

miles,  or  a  little  over  eleven  times  that  of  the  earth. 

These  values  are  from  the  recent  measures  of  Barnard  and  See,  and  are 
notably  larger  than  those  determined  by  earlier  observers  with  a  double- 
image  micrometer  and  given  in  the  table  in  the  Appendix.  Very  likely  the 
truth  may  lie  intermediate. 

The  oblateness  is  ^  ,  —  very  much  greater  than  that  of  any 
other  planet,  Saturn  excepted. 

Its  surface  is  122,  and  its  volume  or  bulk  1355,  times  that 
of  the  earth.  It  is  by  far  the  largest  of  all  planets,  —  larger,  in 
fact,  than  all  the  rest  united. 

Its  mass  is  very  accurately  known,   both  by  means  of  its  its  mass  317 
satellites  and  by  the  perturbations  which  it  produces  upon  cer-  times  that 

^  of  the  earth. 

tain  asteroids.      It  is  77-7777;-^  °^  the  sun's  mass,  or  about  317 
1048.  o5 

times  that  of  the  earth. 

Comparing  this  with  its  volume,  we  find  its  mean  density 
to  be  0.23,  i.e.,  less  than  one  fourth  the  density  of  the  earth  its  density 
and  a  little  less  than  that  of  the  sun.     Its  surface  gravity  is  and  surface 

gravity. 

about  two  and  two-thirds  times  that  of  the  earth,  but  varies 
nearly  twenty  per  cent  between  the  equator  and  poles  of  the 
planet. 

433.    General  Telescopic  Aspect,  Albedo,  etc.  —  In  even  a  small  General 
telescope  the  planet  is  a  fine  object,  since  a  magnifying  power  asPect< 
of  only  60  makes  its  apparent  diameter,  even  when  remotest, 
equal  to  that  of  the  moon.     With  a  large  instrument  and  mag- 
nifying power  of  300  or  400  the  disk  is  covered  with  an  infinite 
variety  of  detail,  interesting  in  outline,  rich  in  color,  —  mostly 
reds  and  brown,  with  here  and  there  an  olive-green,  —  and  these 
details  change  continually  as  the  planet  turns  on  its  axis. 

For  the   most  part,  the  markings  are  arranged  in  "  belts  "  The  belts. 
parallel  to  the  planet's  equator,  as  shown  in  Fig.  147.     The 


384 


MANUAL   OF   ASTRONOMY 


left-hand  one  of  the  two  larger  figures  is  from  a  drawing  by 
Trouvelot  (1870),  and  the  other  from  one  by  Vogel  (1880). 
The  smaller  figure  below  represents  the  planet's  ordinary 
appearance  in  a  3-inch  telescope.  Fig.  148  is  from  a  beauti- 
ful drawing  by  Keeler,  made  in  1889,  which  still  continues  to 


FIG.  147.  —  Telescopic  Views  of  Jupiter 

be  an  excellent  representation  of  the  planet's  aspect.  Near  the 
limb  of  the  planet  the  light  is  less  brilliant  than  in  the  center 
of  the  disk,  and  the  belts  there  fade  out. 

The  planet  shows  no  perceptible  phases,  but  at  quadrature 
the  edge  which  is  turned  away  from  the  sun  is  sensibly  darker 
than  the  other. 

According  to  Zollner,  the  mean  albedo  of  the  planet  is  0.62, 
which  is  very  high,  that  of  white  paper  being  0.78.  The  ques- 
tion has  been  raised  whether  Jupiter  is  not  to  some  extent  self- 
luminous,  but  there  is  no  proof,  and  little  probability,  that  such 
is  the  case. 


THE  MAJOR  PLANETS 


385 


Fio.  148.— Jupiter 
After  drawings  by  Keeler,  at  Lick  Observatory 


386 


MANUAL   OF   ASTRONOMY 


The  planet's 
atmosphere. 


Spectrum 
of  the 
planet. 
Shadings  in 
the  red  and 
orange. 


Rotation 
period  about 
9h55m. 
Different 
for  different 
classes  of 
markings. 


434.  Atmosphere  and  Spectrum.  —  The  planet's  atmosphere 
must  be  very  extensive.     The  forms  visible  with  the  telescope 
are  nearly  all  evidently  "  atmospheric,"   —i.e.,  like  clouds,  —  as 
is  obvious  from  their  rapid  changes,  though  Professor  Hough 
considers  that  we  see  the  pasty,  semi-liquid  surface  of  the  globe 
itself  at  times.     The  low  mean  density  of  the  planet  makes  it, 
however,  very  doubtful  whether  there  is  anything  solid  about  it 
anywhere,  —  whether  it  is  anything  more  than  a  ball  of  fluid, 
overlaid  by  cloud  and  vapor. 

The  spectrum  of  the  planet  differs  less  from  that  of  mere 
reflected  sunlight  than  might  have  been  expected,  showing  that 
the  light  is  not  obliged  to  penetrate  the  atmosphere  to  any  great 
depth  before  it  is  reflected  towards  us  from  the  clouds.  There 
are,  however,  faint  shadings  in  the  red  and  orange  parts  of  the 
spectrum  that  are  probably  due  to  some  unidentified  constituent 
of  the  planet's  atmosphere ;  they  seem  to  be  identical  in  position 
with  certain  bands  which  are  intense  in  the  spectra  of  Uranus 
and  Neptune. 

435,  Rotation.  —  Jupiter  rotates  on  its  axis  more  swiftly  than 
any  other  planet,  —  in  about  9h55m.      The  time  can  be  given 
only  approximately;  not  because  it  is  difficult  to  find,  and  to 
observe  with  accuracy,   well-defined  objects  on  the  disk,  but 
because  different  results  are  obtained  from  different  spots,  rang- 
ing all  the  way  from  9h50m  for  certain  small  bright  spots  to 
9h56im  for  others  of  a  different  character.    Well-marked  features 
near  each  other  on  the  planet's  surface  often  drift  by  each  other, 
sometimes  at  the  rate  of  from  200  to  400  miles  an  hour. 

On  the  whole,  spots  near  the  equator  usually  show  a  shorter 
period  than  those  in  higher  latitudes,  but  there  are  numerous 
exceptions.  There  is  no  such  regular  difference  as  on  the  sun, 
but  there  apparently  are  a  number  of  different  zones,  each  with 
its  own  rate  of  rotation,  and  one  or  two  of  the  swiftest  are  not 
near  the  equator ;  neither  are  the  two  hemispheres,  the  northern 
and  southern,  alike  in  their  behavior. 


THE  MAJOR   PLANETS  387 

The  plane  of  rotation  nearly  coincides  with  that  of  the  orbit,  Plane  of 
the  inclination  being  only  3°,  so  that  there  -can  be  no  well-  rotatlon 

nearly  in 

marked  seasons  on  the  planet  due  to  causes  such  as  produce  plane  of 
our  own  seasons.  orbit> 

436.  Physical  Condition;  the  "  Great  Red  Spot."  —  The  con- 
dition of  the  planet  is  obviously  very  different  from  that  of  the 

earth  or  Mars.      No  permanent  markings  are  found  upon  the  No  perma- 
disk,  though  there  are  some  which  may  be  called  at  least  sub-  nent ;surface 

.  markings. 

permanent,  persisting  for  years  with  only  slight  apparent  change. 

The  most  remarkable  instance  of  such  a  marking  is  the  great  The  great 
red  spot,  shown  in  Figs.  147  and  148.     It  was  first  noted  in  redsPot- 
1878,  was  extremely  conspicuous  for  several  years,  and  then 
gradually  faded  away,  slightly  changing  its  form  and  becoming 
rounder;  even  yet  (1909),  while  hardly  visible  itself,  the  place 
which  it  occupies  is  clearly  marked  by  the  "bed"  it  has  hol- 
lowed out  in  the  great  southern  belt.     In  its  prime  it  was  about 
30000  miles  long  by  about  7000  wide. 

Were  it  not  that  during  the  first  six  or  seven  years  of  its 
visibility  it  lengthened  its  rotation  period  by  about  six  seconds 
(from  9h55m358  to  9h55m418),  we  might  suppose  it  permanently 
attached  to  a  solid  nucleus  below;  but  this  change  of  rotation 
means  that,  relative  to  its  position  in  1878,  the  spot  must  have 
traveled  completely  around  the  nucleus  of  the  planet  in  the  six 
years,  unless  the  nucleus  itself  changed  its  own  period  to  the 
same  extent,  and  that  without  affecting  the  motions  of  the  other 
spots  and  markings. 

No  really  satisfactory  explanation  of  the  spot  and  its  strange 
behavior  has  yet  been  found. 

437.  Temperature.  —  Many  things  about  the  planet  indicate  Temper- 

a  probable  high  temperature,  as,  for  instance,  the  abundance  of  ature  Pro°- 
clouds  and  the  rapidity  of  their  motions  and  transformations,  The  planet 
which  almost  certainly  indicate  a  rapid  exchange  of  matter  and  a  semi-sun< 
a  vigorous  vertical  circulation  between  the   surface   and  the 
underlying  nucleus,   if  there  is  one.     To   maintain    such   an 


388 


MANUAL   OF   ASTRONOMY 


The  seven 
satellites  of 
Jupiter ; 
their  dis- 
covery. 


The  fifth 
satellite. 


Data  relat- 
ing to  the 
Galilean 
satellites. 


Third  satel- 
lite the 
largest. 

Peculiarities 
of  the  fourth 
satellite : 
very  dark 
surface. 


ebullition  requires  a  continuous  supply  of  heat,  and  since  on 
Jupiter  the  solar  light  and  heat  are  only  ^T  as  intense  as  here,  we 
are  forced  to  conclude  that  it  gets  very  little  of  its  heat  from  the 
sun,  but  is  probably  hot  on  its  own  account,  and  for  the  same 
reason  that  the  sun  is  hot,  i.e.,  as  the  result  of  a  process  of  con- 
densation. In  short,  it  appears  very  probable,  as  has  been  inti- 
mated before,  that  the  planet  is  a  sort  of  "  semi-sun,"  -  -  hot, 
though  not  so  hot  as  to  be  sensibly  self-luminous. 

438.  Satellites.  —  Jupiter  has  eight1  satellites,  four  of  them  so 
large  as  to  be  seen  easily  with  a  common  opera-glass.  These 
were  in  a  sense  the  first  heavenly  bodies  ever  "  discovered," 
having  been  found  by  Galileo  in  January,  1610,  with  his  newly 
invented  telescope.  The  fifth  satellite,  discovered  by  Barnard 
at  the  Lick  Observatory  in  1892,  is,  on  the  other  hand,  extremely 
small  and  visible  only  in  the  most  powerful  instruments. 

It  is  nearest  to  the  planet,  its  distance  from  the  center  of  Jupi- 
ter being  only  112500  miles  and  its  sidereal  period  Ilh57m.4. 
Its  diameter  probably  does  not  exceed  100  miles. 

The  old  satellites,  though  more  remote,  are  still  usually  known 
as  the  first,  second,  etc.,  in  the  order  of  their  distance  from  the 
planet.  Their  distances  range  from  262000  to  1 169000  miles 
and  their  sidereal  periods  from  forty-two  hours  to  sixteen  and 
two-thirds  days.  Their  orbits  are  almost  perfectly  circular 
and  lie  very  nearly  in  the  plane  of  the  planet's  equator.  The 
third  satellite  is  much  the  largest,  having  a  diameter  of  about 
3600  miles,  while  the  others  are  between  2000  and  3000,  —  all 
of  them  larger  than  our  moon,  though  much  less  massive. 

For  some  reason,  the  fourth  satellite  is  a  very  dark-com- 
plexioned body,  so  that  when  it  crosses  the  planet's  disk  it 
looks  like  a  black  spot,  hardly  distinguishable  from  its  own 
shadow;  the  others  under  similar  circumstances  appear  bright, 
dark,  or  are  invisible,  according  to  the  brightness  of  the  part  of 
the  planet  which  happens  to  form  the  background.  With  very 
powerful  instruments  spots  are  sometimes  visible  on  their 
1  For  the  sixth,  seventh,  and  eighth  satellites,  see  note  on  page  408. 


THE   MAJOR   PLANETS  389 

surfaces,  and  there  are  variations  in  their  brightness;  W.  H. 
Pickering,  Douglass,  and  some  other  observers  have  also  reported 
periodic  irregularities  in  their  forms,  as  if  they  were  cloudlike 
in  constitution. 

In  the  case  of  the  fourth  satellite  the  regularity  in  the  changes 
of  brightness  indicates  that  it  follows  the  example  of  our  moon 
in  always  keeping  the  same  face  towards  the  planet,  and  the  Keeps  same 
observations  of  Douglass  at  Flagstaff,  in  1897,  of  spots  upon  the  ^^ 
surfaces  of  the  third  and  fourth  satellites  also  indicate  a  rotation  during  its 
agreeing  with  their  orbital  periods  far  within  the  limits  of  error  rotatlon- 
to  be  expected  in  such  observations.     It  may  be  considered  prac- 
tically certain  that  both  these  satellites  behave  like  our  moon. 

The  four  satellites  of  Galileo  have  names  also :  viz.,  lo,  Europa,  Gany-   Names  of 

mede,  and  Callisto,  —  lo  being  the  nearest  to  the  planet.    But  these  names   Galilean 
, ,  satellites, 

are  seldom  used. 

439.   Eclipses  and  Transits.  —  The  orbits  of  the  satellites  are  Eclipses  and 
so  nearlv  in  the  plane  of  the  planet's  orbit  that  with  the  excep-  transits  of 

J  r     the  satel- 

tion  of  the   fourth,  which  at  certain  times  escapes,  they  are  Htes. 
eclipsed  at  every  revolution,  and  also  cross  the  planet's  disk  at 
every  conjunction. 

When  the  planet  is  either  at  opposition  or  conjunction  the 
shadow,  of  course,  is  directly  behind  it,  and  we  cannot  see  the 
eclipse  at  all.  At  other  times  we  ordinarily  see  only  the  begin- 
ning or  the  end ;  but  when  the  planet  is  at  or  near  quadrature 
the  shadow  projects  so  far  to  one  side  that  the  whole  eclipse  of 
every  satellite,  except  the  first,  takes  place  clear  of  the  disk. 

An  eclipse  is  a  gradual  phenomenon,  the  satellite  disappear-  The  phe- 
ing  by  becoming  slowly  fainter  and  fainter  as  it  plunges  into 
the  shadow,  and  reappearing  in  the  same  leisurely  way. 

Two  important  uses  have  been  made  of  these  eclipses :  they  Their  use  in 
have  been  employed  for  the  determination  of  longitude,  and  astronomy- 
they  furnish  the  means  of  ascertaining  the  time  required  by  light 
to  traverse  the  space  between  the  earth  and  the  sun. 


390 


MANUAL  OF   ASTRONOMY 


440,  The  Equation  of  Light — When  we  observe  a  celestial 
body  we  see  it,  not  as  it  is  at  the  moment  of  observation,  but  as 
it  was  at  the  moment  when  the  light  which  we  see  left  it.     If 
we  know  its  distance  in  astronomical  units,  and  know  how  lon£ 
light  takes  to  traverse  that  unit,  we  can  at  once  correct  our 
observation  by  simply  dating  it  back  to  the  time  when  the  light 
started  from  the  object. 

The  necessary  correction  is  called  the  Equation  of  Light,  and 
the  time  required  by  light  to  traverse  the  astronomical  unit  of 
distance  is  the  Constant  of  the  light-equation  (not  quite  five 
hundred  seconds,  as  we  shall  see). 

It  was  in  1675  that  Roemer,  the  Danish  astronomer  (the  inventor  of  the 
transit-instrument,  meridian-circle,  and  prime  vertical  instrument,  —  a  man 
almost  a  century  in  advance  of  his  day),  found  that  the  eclipses  of  Jupiter's 
satellites  show  a  peculiar  variation  in  their  times  of  occurrence,  which  he 
explained  as  due  to  the  time  taken  by  light  to  pass  through  space.  His  bold 
and  original  suggestion  was  neglected  for  more  than  fifty  years,  until  long 
after  his  death,  when  Bradley's  discovery  of  aberration  proved  the  correct- 
ness of  his  views. 

441,  Eclipses  of  the  satellites  recur  at  intervals  which  are  really 
almost  exactly  equal  (the  perturbations  being  very  slight),  and 
the  interval  can  easily  be  determined  and  the  times  tabulated. 
But  if  we  thus  predict  the  times  of  the  eclipses  during  a  whole 
synodic  period  of  the  planet,  then,  beginning  at  the  time  of  oppo- 
sition, it  is  found  that  as  the  planet  recedes  from  the  earth  the 
eclipses,  as  observed,  fall  constantly  more  and  more  behindhand, 
and  by  precisely  the  same  amount  for  all  four  satellites.    The  dif- 
ference between  the  predicted  and  observed  time  continues  to  in- 
crease until  the  planet  is  near  conjunction,  when  the  eclipses  are 
almost  seventeen  minutes  later  than  the  prediction.     After  the 
conjunction  they  quicken  their  pace  and  make  up  the  loss,  so  that 
when  opposition  is  reached  once  more  they  are  again  on  time. 

It  is  easy  to  see  from  Fig.  149  that  at  opposition  the  planet 
is  nearer  the  earth  than  at  conjunction  by  just  two  astronomical 


THE   MAJOR   PLANETS 


391 


units,  i.e.,  JB  —  JA  =  2  SA.  Light  coining  from  J  to  the  earth 
when  it  is  at  A  will,  therefore,  make  the  journey  quicker  than 
when  it  is  at  B,  by  twice  the  time  it  takes  light  to  pass  from  S 
to  A,  provided  it  moves  through  space  at  a  uniform  rate,  as 
there  is  every  reason  to  believe. 

The  whole  apparent  retardation  of  eclipses  between  opposi- 
tion and  conjunction  must,  therefore,  be  exactly  twice  the  time 
required  for  light  to  come  from 
the  sun  'to  the  earth.     In  this 
way  the  "  light-equation  con- 
stant"  is  found  to  be  very 
nearly  499  seconds,  or  8m198, 
with  a  probable  error  of  per- 
haps two  seconds. 

Attention  is  specially  di- 
rected to  the  point  that  the 
observations  of  the  eclipses 
of  Jupiter's  satellites  give 
directly  neither  the  velocity 

of  light  nor  the  distance  of  the 

,1  .  ,      ,1       ..          FIG.  149.  — Determination  of  the  Equation 

sun  ;  they  give  only  the  time  of  Light 

required   by   light    to    make 

the  journey  from  the  sun.  Many  elementary  text-books,  espe- 
cially the  older  ones,  state  the  case  carelessly. 

Since  these  eclipses  are  gradual  phenomena,  the  determination  of  the 
exact  moment  of  a  satellite's  disappearance  or  reappearance  is  very 
difficult,  and  this  renders  the  result  somewhat  uncertain.  Prof.  E.  C. 
Pickering  of  Cambridge  has  proposed  to  utilize  photometric  observations 
for  the  purpose  of  making  the  determination  more  precise,  and  two  series 
of  observations  of  this  sort  and  for  this  purpose  are  now  completed,  and 
are  being  reduced,  one  in  Cambridge,  and  the  other  in  Paris  under  the 
direction  of  Cornu,  who  devised  a  similar  plan.  Pickering  has  also  applied 
photography  to  the  observation  of  these  eclipses  with  encouraging  success. 

442.  The  Distance  of  the  Sun  determined  by  the  "Light- 
Equation." —  Until  1849  our  only  knowledge  of  the  velocity  of 


How  this 
determines 
the  constant 
of  the  light- 
equation. 


The  con- 
stant, 
499»  *  2*. 


Photometric 
method  of 
observing 
the  eclipses. 


892 


MANUAL   OF   ASTRONOMY 


Distance  of 
sun  obtained 
by  multiply- 
ing the 
constant  of 
the  light- 
equation  by 
the  velocity 
of  light. 


light  was  obtained  from  such  observations  of  Jupiter's  satellites. 
By  assuming  as  known  the  earths  distance  from  the  sun,  the 
velocity  of  light  can  be  obtained  when  we  know  the  time  occu- 
pied by  light  in  coming  from  the  sun.  At  present,  however, 
the  case  is  reversed.  We  can  determine  the  velocity  of  light 
by  two  independent  experimental  methods,  and  with  a  surpris- 
ing degree  of  accuracy.  Then,  knowing  this  velocity  and  the 
"light-equation  constant,"  we  can  deduce  the  distance  of  the  sun. 
According  to  the  latest  determinations,  the  velocity  of 'light  is 
186330  miles  per  second.  Multiplying  this  by  499,  we  get 
92  979000  miles  for  the  sun's  distance.  (Compare  Sec.  173.) 


Saturn:  its 
brightness 
and  varia- 
tions of 
its  light. 


Orbital 
peculiari- 
ties. 


SATUKN 

443.  Saturn  is  the  most  remote  of  the  planets  known  to  the 
ancients.    In  brilliance  it  is  inferior  to  Venus  and  Jupiter,  or  even 
Mars  when  nearest;  still,  it  is  a  conspicuous  object  of  the  first 
magnitude,  outshining  all  the  stars  (except  Sirius)  with  a  steady, 
yellowish  radiance,  not  varying  much  in  appearance  from  month 
to  month,  though  in  the  course  of  fifteen  years  it  alternately 
gains  and  loses  nearly  fifty  per  cent  of  its  brightness  with  the 
changing  phases  of  its  rings ;  for  it  is  unique  among  the  heavenly 
bodies,  a  great  globe  attended  by  a  retinue  of  ten  satellites, 
and  surrounded  by  a  system  of  rings  which  has  no  counterpart 
elsewhere  in  the  universe,  so  far  as  known  at  present. 

444.  Orbit. —  Its  mean  distance  from  the  sun  is  about  nine 
and  one-half  astronomical  units,  or  886  000000  miles ;  but  the 
distance  varies  nearly  100  000000,  on  account  of  the  consider- 
able eccentricity  of   the  orbit   (0.056).     Its  nearest  opposition 
approach  to  the  earth  is  about  774  00 00 00  miles,  while  at  the 
remotest  conjunction  it  is  1028  000000  mites  away. 

The  sidereal  period  of  the  planet  is  about  twenty-nine  and 
one-half  years,  the  synodic  being  378  days.  The  inclination  of 
the  orbit  to  the  ecliptic  is  about  2£°. 


THE  MAJOR  PLANETS  393 

445,  Dimensions,  Mass,  etc. — The  apparent  mean  diameter  of  Diameter, 
the  planet  varies,  according  to  the  distance,  from  14"  to  20".  Jjjjjjj8^ 
The  equatorial  diameter  is  about  76500  miles,  the  polar  diame-  volume! 
ter  only  69800  ;  the  mean  diameter,  therefore,  is  about  74000, 

-  a  little  more  than  nine  times  the  diameter  of  the  earth.  The 
oblateness  of  Saturn  (the  flattening  at  the  poles)  is  nearly  ^, 
being  greater  than  that  of  any  other  planet. 

The  surface  is  about  eighty-six  times  that  of  the  earth,  and 
its  volume  about  800. 

Its  mass  is  found  by  means  of  its  satellites  to  be  ninety-five  Mass, 
times  that  of  the  earth,  so  that  its  mean  density  comes  out^nly  density»  and 

SliriRC6 

one  eighth  that  of  the  earth,  —  only  two  thirds  that  of  water  !  gravity. 
It  is  by  far  the  least  dense  of  all  the  planetary  family.     Its  Saturn  less 

.   _.  .  dense  than 

mean  superficial  gravity  is  about  1.2  times  gravity  upon  the  water. 

earth,  varying,  however,  nearly  twenty-five  per  cent  between 
the  equator  and  the  pole. 

The  rotation  period  is  about  10h14m,  as  determined  by  Pro-  Rotation 
fessor  Hall  in  1876  from  a  white  spot  that  appeared  near  the 
planet's  equator  and  continued  visible  for  several  weeks.  Later 
observations  of  Stanley  Williams  in  1893,  while  confirming  this 
result,  indicate  that  there  are  vigorous  surface  currents,  as  on 
Jupiter,  so  that  different  spots  give  different  rotation  periods. 
A  northern  spot  observed  in  1903  gave  10h38ra. 

The  equator  of  the  planet  is  inclined  about  27°  to  the  plane  its  equator 

Of  the  Orbit.  inclined  27o 

to  plane  of 

446.  Surface,  Albedo,  Spectrum. — The  disk  of  the  planet,  like  its  orbit, 
that  of  Jupiter  and  the  sun,  is  darker  at  the  edge,  and,  like  that 

of  Jupiter,  it  shows  a  number  of  belts  arranged  parallel  to  the 
equator.  The  equatorial  belt  is  very  much  brighter  than  the 
rest  of  the  surface  (not  quite  so  much  so,  however,  as  repre- 
sented in  Fig.  150),  and  is  often  of  a  delicate  pinkish  tinge. 
The  belts  in  higher  latitudes  are  comparatively  faint  and 
narrow,  while  just  at  the  pole  there  is  a  dark  cap,  sometimes  dis- 
tinctly olive-green  in  color.  Compared  with  Jupiter,  however, 


394 


MANUAL   OF   ASTRONOMY 


there    is    very    little    detail   observable   on   the   surface ;   the 
edges  of  the  belts  are  usually  smooth,  with  only  occasional 


FIG.  150.  —  Saturn 
After  Proctor 


irregularities,  and  the  spots,  when  they  appear,  are  as  a  rule  ill- 
defined  and  very  faintly  contrasted  with  the  background,  so 
that  they  are  difficult  to  observe.  Like  the  markings  on 


THE   MAJOR   PLANETS  395 

Jupiter,  they  are  almost  certainly  atmospheric,  i.e.,  clouds  of 
no  great  density. 

The  mean  albedo  of  the  planet  is  0.52,  according  to  Zollner,  Albedo  0.52. 
—  very  nearly  the  same  as  that  of  Venus. 

The  spectrum  of  Saturn  is  substantially  like  that  of  Jupiter, '  Spectrum  of 
but  the  dark  bands  in  the  lower  part  of  the  spectrum  are  more  the  Planet- 

Bands  more 

pronounced.      These  bands,  which  are  doubtless  due  to  some  pronounced 
unidentified  constituent  of  the  planet's  atmosphere,  do  not  appear,  than  in  case 
however,  in  the  spectrum  of  the  rings,  which  presumably  have 
very  little  atmosphere  upon  them. 

As  to  the  physical  condition  and  constitution  of  the  planet,  Probably 
it  is  probably  essentially  like  that  of  Jupiter,  though  still  farther  ^^[om 
from  solidity ;  it  does  not,  however,  seem  to  boil  quite  so  vigor-  sources, 
ously  at  the  surface.     Its  supply  of  solar  heat  and  light  is  less 
than  -1-Q  of  that  which  we  receive  on  the  earth. 

447.   The  Rings.  —  The  most  remarkable  peculiarity  of  the 
planet  is  its  ring  system.    The  globe  is  surrounded  by  three  thin,  its  ring 
flat,  concentric  rings  in  the  plane  of  Saturn's  equator,  like  cir-  system- 
cular  disks  of  paper  perforated    through   the    center.      They 
are  generally  referred  to  as  A,  B,  and  C,  A  being  the  exterior 
ring. 

Galileo  half  discovered  them  in  1610;  that  is,  he  saw  with  Haifdis- 
his  little  telescope  two  appendages  on  each  side  of  the  planet,  Covered  by 
but  he  could  make  nothing  of  them,  and  after  a  while  he  lost 
them,  to  regain  them  again  some  years  later,  greatly  to  his 
perplexity. 

The  problem  remained  unsolved  for  nearly  fifty  years,  until  Discovery 
Huyghens  explained  the  mystery  in  1655.     Twenty  years  later  £°n^>ueted 
D.  Cassini  discovered  that  the  ring  is  double,  i.e.,  composed  of  ghensand 
two  concentric  rings,  with  a  dark  line  of  separation  between  D-  Cassim- 
them,  and  in  1850,  Bond  of  Cambridge,  U.S.,  discovered  the 
third  "dusky"  or  " gauze"  ring  between  the  principal  ring  and  Gauze  ring 
the  planet.     '(It  was  discovered  a  fortnight  later,  and  inde-  disc°vered 

r  v  by  Bond 

pendently,  by  Dawes  in  England.)  in  i860. 


396 


MANUAL   OF   ASTRONOMY 


The  outer  ring,  A,  has  an  exterior  diameter  of  about  173000 
miles  and  a  width  of  not  quite  12000.  Cassini's  division 
between  this  and  B  is  about  1800  miles  wide;  the  ring  B,  much 
of  the  rings.  the  Broadest  and  brightest  of  the  three,  has  a  breadth  of  about 
17000  miles.  The  semi-transparent  ring,  (7,  has  a  width  of 
about  11000  miles,  leaving  a  clear  space  of  from  7000  to 
8000  miles  in  width  between  the  planet's  equator  and  its  inner 
edge.  Their  thickness  is  exceedingly  small, — probably  less 
than  50  miles.  (These  dimensions  are  from  the  recent  measure- 
ments of  Professor  See  and  differ  slightly  from  those  given  in 


FIG.  151.  — The  Phases  of  Saturn's  Rings 

the  G-eneral  Astronomy.)  There  is  some  reason  to  suspect  that 
the  rings  may  have  changed  their  dimensions  at  different  times, 
but  as  yet  the  proof  is  insufficient. 

448.  Phases  of  the  Rings.  —  The  rings  are  inclined  about  28° 
to  the  ecliptic  (27°  to  the  planet's  orbit),  having  their  nodes  in 
longitude  168°  and  348°,  and  of  course  maintain  their  plane 
parallel  to  itself  at  all  times.  Twice  in  a  revolution  of  the 
planet  (once  in  about  fifteen  years)  this  plane  sweeps  across  the 
orbit  of  the  earth  (too  small  to  be  shown  in  Fig.  151),  occupy- 
ing not  quite  a  year  in  so  doing;  and  whenever  the  plane  passes 
between  the  earth  and  the  sun  the  dark  side  of  the  ring  is 
towards  us  and  the  edge  alone  is  visible.  The  plane  of  the 


THE   MAJOR   PLANETS  397 

ring  traverses  the  orbit  of  the  earth  in  about  359.6  days,  and 
during  this  time  the  earth  herself  passes  the  plane  either  once 
or  three  times,  according  to  circumstances, — usually  three  times, 
thus  causing  two  periods  of  disappearance  during  the  critical 
year.  When  the  earth  is  crossing  the  plane  of  the  ring,  so  that 
its  edge  is  exactly  towards  us,  the  ring  becomes  absolutely 
invisible  to  all  existing  telescopes  for  several  days;  and  in  the 
longer  periods,  while  the  dark  side  of  the  ring  is  presented  to 
us, — sometimes  for  several  weeks,  —  only  the  most  powerful 
instruments  can  see  it,  like  a  fine  needle  of  light  piercing  the 
planet's  ball,  and  with  satellites  strung  like  beads  upon  it. 
The  last  disappearance  occurred  in  1907. 

449,   The   Structure  of  the   Rings. — It   is    now  universally  structure  of 
admitted  that  the  rings  are  not  continuous  sheets,  either  solid  or  the  rm&s: 

a  swarm  of 
liquid,  but  a  flock  or  swarm  of  separate  particles,  little  umoon-  independent 

lets,"  each  pursuing  its  own  independent  circular  orbit  around  moonlets- 
the  planet,  though  all  moving  nearly  in  the  same  plane. 

The  idea  was  first  suggested  by  J.  Cassini  in  1715,  and  later  by  Wright 
in  1750,  but  was  quite  lost  sight  of  until  brought  forward  again  by  G.  P. 
Bond  in  connection  with  his  father's  discovery  of  the  dusky  ring.     Peirce   Origin  and 
soon  demonstrated  that  the  rings  could  not  be  solid,  though  he  was  dis-  develop- 
posed  to  think  they  might  be  liquid.    Clerk  Maxwell  in  1857  went  further,   ment  of  the 
by  showing  mathematically  that  while  they  could  be  neither  solid  nor 
liquid,  they  must,  in  order  to  be  permanent,  be  constituted  as  explained 
above. 

There  are  also  observational  facts  that  confirm  the  theory.  Photometric 
Seeliger  has  shown  that  the  variations  in  the  naked-eye  bright-  observa- 
ness  of  the  planet,  due  to  the  phases  of  the  rings,  can  be  explained  Seeliger  and 
only  on  the  hypothesis  that  they  are  like  clouds  of  dust.     Again,  Barnard. 
in  1892  Barnard  observed  the  satellite  lapetus  during  one  of 
its  eclipses  (a  very  rare  event)  and  found  that  the  shadow  of 
the  dusky  ring  is  not  opaque ;  the  satellite  did  not  disappear 
when  immersed  in  it,  but  vanished  as  soon  as  it  entered  the 
shadow  of  the  bright  rings. 


398 


MANUAL   OF   ASTRONOMY 


Keeler's 
spectro- 
scopic  proof 
that  the 
outer  edge 
of  the  ring 
moves  more 
slowly  than 
the  inner. 


Effect  of 
reflection  on 
shift  of 
spectrum 
lines. 


Illh^eter 


450,  Keeler's  Demonstration  of  the  Meteoric  Theory  of  Saturn's 
Rings.  —  In  1895  Keeler,  then  at  Allegheny,  obtained  spectro- 
scopic  proof  that  the  outer  edge  of  the  ring  revolves  more  slowly 
than  the  inner,  as  the  theory  requires,  but  as  would  not  be  the 
case  if  the  ring  were  a  continuous  sheet.  Photographs  were 
made  of  the  spectrum  of  the  planet  with  the  slit  of  the  spectro- 

scope crossing  the  planet 
i  and  its  rings,  as  shown 

in  Fig.  152,  which  is  a 
much  magnified  draw- 
ing of  the  actual  image. 
At  the  western  limb 
of  the  planet  and  the 
western  extremity  of  the 
ring  the  motion  of  rota- 
tion carries  the  particles 

n.  *• 

from  us,  and  the  dis- 
placement of  the  spec- 
trum lines  should  be 
towards  the  red,  accord- 
ing to  Doppler's  prin- 
ciple ;  moreover,  since 
the  particles  shine  by 
reflected  sunlight,  the 

displacement  is  practically  doubled  at  the  time  of  the  planet's 
opposition,  —  twice  as  great  as  if  the  particles  were  self-luminous. 
On  the  eastern  side  there  is  an  equal  shift  towards  the  violet. 
Now,  on  looking  at  the  diagram  of  the  spectrum  (given  below 
the  planet),  we  see  that  while  at  C  the  line  in  the  spectrum 
is  bodily  displaced  towards  the  red,  as  it  ought  to  be,  the 
displacement  at  the  outer  edge  of  the  ring  is  less  than  that  at 
the  inner,  and  correspondingly  at  A.  This  shows  that  the 
particles  at  the  outer  edge  are  moving  more  slowly  than  at  the 
inner. 


FIG.  152.  —  Spectroscopic  Observation  of 

Saturn's  Ring 

Keeler 


THE   MAJOR   PLANETS  399 

The  fact  is  made  conspicuous  by  its  effect  upon  the  inclina- 
tion of  the  lines:  while  in  the  spectrum  of  the  ball  the  lines 
slope  upwards  towards  the  right,  in  the  ring  spectrum  on  both 
sides  they  slope  the  other  way. 

At  the  inner  edge  of  the  ring  the  observations  indicated  a 
velocity  of  12£  miles  a  second,  at  the  outer  edge  only  10,  — 
precisely  the  velocities  that  satellites  of  Saturn  ought  to  have 
at  the  corresponding  distances  from  the  planet. 

It  may  be  noted  also  that  the  inclination  of  the  lines  on  the  ball  indi- 
cates at  the  edge  of  the  planet  a  velocity  of  6.4  miles  a  second,  correspond- 
ing to  a  rotation  period  -of  10h14m.6,  —  almost  exactly  agreeing  with  that 
deduced  by  Professor  Hall  from  the  observation  of  the  spot. 

The  observations  are  extremely  delicate,  as  the  whole  width  of  the 
spectrum  was  not  quite  a  millimeter,  the  figure  being  magnified  nearly 
fifty  times.  But  Keeler's  results  have  since  been  fully  confirmed  by 
Deslandres,  Belopolsky,  and  Campbell. 

The  investigations  of   H.   Struve   upon  the  motion  of  the  Mass  of 
planet's  satellites  seemed  to  show  that  the  mass  of  the  rings  ri?g.s 
is  inappreciable  ;  but  the  more  recent  work  of  Professor  Hall 


gives  their  mass  as  yy1^  that  of  the  planet,  very  small  indeed 
but  certainly  appreciable. 

451.    Stability  of  the  Ring.  —  If  the  ring  were  solid,  it  cer-  Question  of 
tainly  would  not  be  stable;    it    could  not  endure  the  strains  stabiMty°f 
due  to  its  rotation,  nor  is  it  certain  that  even  the  swarmlike 
structure  makes  it  forever  secure.     There   have  been  strong 
suspicions  of  a  change   in   the  width  of  the  rings  and  their 
divisions,  but  the  latest  measurements  hardly  confirm  the  idea. 
It  is  not,  however,  improbable  that  the  ring  may  ultimately  be 
broken  up. 

It  can  hardly  be  doubted  that  the  details  of  the  ring  are  con- 
tinually changing  to  some  extent;  thus,  the  outer  ring,  J,  is 
occasionally  divided  into  two  by  a  very  narrow  black  line  known 
as  "Encke's  division,"  though  more  usually  there  is  merely  a 
darkish  streak  upon  it  not  amounting  to  a  real  break  in  the 


400  MANUAL   OF   ASTRONOMY 

surface.  When  the  rings  are  edgewise  notable  irregularities 
are  observed  upon  them,  as  if  they  were  not  accurately  plane 
nor  quite  of  even  thickness  throughout.  Irregularities  are 
reported  also  in  the  form  of  the  shadow  cast  by  the  planet  on 
the  rings,  indicating  that  the  ring  surface  is  not  entirely  flat. 

But  caution  must  be  used  in  accepting  and  interpreting  such  observa- 
tions, because  illusions  are  very  apt  to  occur  from  the  least  indistinctness 
of  vision  or  faintness  of  light.  Generally  speaking,  the  writer  has  found 
that  the  better  the  seeing,  the  fewer  abnormal  appearances  are  noted,  and 
the  experience  of  other  observers  with  large  telescopes  is  the  same. 

452.  Satellites.  —  Saturn  has  ten1  of  these  attendants,  the 
iarges^  of  which,  named  Titan,  was  discovered  by  Huyghens 
in  1655.  It  is  easily  seen  with  a  3-inch  telescope. 

D.  Cassini,  with  his  long-focus  telescope  (Sec.  44,  note),  found 
four  others  before  1700 ;  Sir  W.  Herschel  in  1789  discovered 
the  two  which  are  nearest  the  planet;  and  in  1848  the  elder 
Bond  added  an  eighth;  for  the  ninth  see  note  on  next  page. 

As  the  order  of  discovery  does  not  agree  with  that  of  distance, 
it  has  been  found  convenient,  in  order  to  avoid  confusion,  to 
adopt  names  for  the  satellites  (suggested  by  Sir  John  Herschel). 
They  are,  beginning  with  the  most  remote, 

Their  Iap8tus,  (Hyperion),  Titan  ;  Rhea,  Dione,  Tethys ;  Enceladus,  Mimas, 

names. 

Leaving  out  Hyperion  (which  had  not  been  discovered  when 

the  names  were  first  assigned),  they  form  a  line  and  a  half  of  a 

regular  Latin  pentameter. 

The  range  of  the  system  is  enormous.     lapgtus  is  at  a  distance 

of  2  225000  miles,  with  a  period  of  seventy-nine  days,  —  nearly 
Peculiarities  as  long  as  that  of  Mercury.  On  the  western  side  of  Saturn  this 
of  lapetus.  satellite  is  always  much  brighter  than  at  the  eastern,  showing  that, 

like  our  own  moon,  it  always  keeps  the  same  face  towards  the 

planet,  —  one  half  of  its  surface  being  darker  than  the  other. 
Titan.  Titan,  as  its  name  suggests,  is  by  far  the  largest.    Its  distance 

is  about  770000  miles  and  its  period  a  little  less  than  sixteen 
i  For  the  tenth  satellite  see  note  on  page  408. 


THE   MAJOR   PLANETS  401 

days.  Its  diameter,  as  measured  by  Barnard,  is  2720  miles.  Its 
mass  is  found,  from  the  perturbations  produced  by  it  in  the 
motion  of  the  other  satellites,  to  be  ^gVo  °f  Saturn's. 

The  orbit  of  lapetus  is  inclined  about  10°  to  the  plane  of  the 
rings,  but  all  of  the  other  satellites  move  sensibly  in  their  plane, 
and  all  the  five  inner  ones  in  orbits  sensibly  circular. 

Early  in  1899  Prof.  W.  H.  Pickering  announced  the  discovery  of  a 
ninth  satellite  (to  which  he  has  assigned  the  name  of  Phoebe),  found  on 
photographs  made  at  Arequipa,  the  southern  annex  of  the  Harvard  College   Phoebe,  a 
Observatory.     The  discovery  remained  long  unverified,  but  early  in  1904  ninth 
the  satellite  was  rediscovered  on  a  number  of  recent  Arequipa  negatives,   8 
and    its  orbit  determined.     Its  distance  from  Saturn  is  about  8  000000 
miles,  its  period   546.5  days.     Its  motion  is  nearly  in  the  plane  of  the 
ecliptic,  but  retrograde.    It  is  perhaps  200  miles  in  diameter,  and  so  faint 
as  to  be  invisible  in  any  but  the  most  powerful  telescopes. 

URANUS 

• 

453.    Discovery  of  Uranus.  —  Uranus  was  the  first  planet  ever  Discovery 
"  discovered,"  and  the  discovery  created  great  excitement  and  °f 
brought  the  highest  honors  to  the  astronomer.     It  was  found  m 
accidentally  by  the  elder  Herschel  on  March  13,  1781,  while 
"sweeping"  the  heavens  for  interesting  objects  with  a  7-inch 
reflector  of  his  own  construction.     He  recognized  it  at  once  by 
its  disk  as  something  different  from  a  star,  but  never  dreaming 
of  a  new  planet  supposed  it  to  be  a  peculiar  kind  of  comet ;  its 
planetary  character  was  not  demonstrated  until  nearly  a  year 
had  passed,  when  Lexell  of  St.  Petersburg  showed  by  his  calcu- 
lations that  it  was  doubtless  a  planet  beyond  Saturn,  moving  in 
a  nearly  circular  orbit. 

It  is  easily  visible  to  a  good  eye  on  a  moonless  night  as  a 
star  of  the  sixth  magnitude. 

The  name  of  Uranus,  suggested  by  Bode,  finally  prevailed 
over  other  appellations  that  were  proposed  (Herschel  had  called 
it  the  "Georgium  Sidus,"  in  honor  of  the  king). 


402 


MANUAL   OF   ASTRONOMY 


Previous 
observa- 
tions of  the 
planet. 


Data  relat- 
ing to  its 
orbit. 


Diameter 
and  bulk  of 
the  planet. 


Its  mass  and 
density. 


>lbedo  and 
spectrum. 


It  was  found  on  reckoning  backward  that  the  planet  had  been 
many  times  observed  as  a  star  and  had  barely  missed  discovery 
on  several  previous  occasions.  Twelve  observations  of  it  had 
been  made  by  Lemonnier  alone,  and  later  they  proved  extremely 
valuable  in  connection  with  the  investigations  which  led  to  the 
discovery  of  Neptune. 

454.  Orbit  of  Uranus.  —  The  mean  distance  of  the  planet  from 
the  sun  is  19.2  astronomical  units,  or  1782  000000  miles.     The 
sidereal  period  is  eighty-four  years  and  the  synodic  36  9£  days, 
the  annual  advance  of  the  planet  among  the  stars  being  only 
a  little  over  4i°.     The  eccentricity  of  the   orbit  is  about  the 
same  as  that  of  Jupiter,  the  sun  being  83  000000  out  of  the 
center  of  the  orbit.     The  inclination  of  the  orbit  to  the  ecliptic 
is  only  46'.     The  light  and  heat  received  from  the  sun  are  only 
about  -^-Q  of  that  received  by  us. 

455.  The  Planet  itself.  —  In  the  telescope  it  shows  a  greenish 
.disk  about  4"  in  diameter,  though  the   measurements  of  See 
make  it  only  3".3,  corresponding  to  a  diameter  of  only  28500 
miles,  which  is  3400  miles  less  than  that  hitherto  generally 
accepted  and  given  in  the  tables  of  the  Appendix.     If  we  admit 
the  correctness  of  this  new  measure,  the  volume  comes  out  only 
forty-seven  times  that  of  the  earth  as  against  the  sixty-five  of 
the  tables.     The  mass  is  determined  much  more  accurately  than 
the  diameter  (by  the  motion  of  its  satellites)  and  is  about  14.6 
times  that  of  the  earth,  the  density  of  the  planet  (still  accepting 
See's  diameter)  being  0.31  of  the  earth  and  its  surface  gravity 
a  little  greater  than  ours,  1.11.     The  albedo  of  the  planet  is 
very  high,  0.62  according  to  Zollner,  even  higher  than  that  of 
Jupiter.     The  spectrum  exhibits  strong  dark  bands  in  the  red, 
due,  doubtless,  to  some  unidentified  substance  in  the  planet's 
probably  dense  atmosphere.     They  explain  the  greenish  tinge 
of  the  planet's  light. 

The  planet's  disk  as  determined  by  various  observers  about 
1882,  when  the  plane  of  the  satellites'  orbits  was  directed 


THE   MAJOR   PLANETS  403 

towards  the  earth,  was  obviously  oval,  indicating  an  oblateness  Obiateness. 
of  about  J^.     At  present  (1902)  the  pole  is  presented  to  us  and 
the  disk  appears  round.     There  are  110  distinct  markings  on  the 
disk,  but  there  are  faint  traces  of  belts,  which  appear  to  lie  not  Belts, 
exactly  in  the  plane  of  the  satellites,  but  at  an  angle  of  some 
15°  or  20°.     They  are  too  indistinct,  however,  to  warrant  any 
positive  assertion.     Nothing  has  yet  been  observed  from  which 
the  rotation  of  the  planet  can  be  determined. 

456.   Satellites.  —  The  planet  has  four  satellites, — Ariel,  Um-  The  four 
briel,  Titania,  and  Oberon,  Ariel  being  the  nearest  to  the  planet.  satellltes- 

The  two  brightest,  Oberon  and  Titania,  were  discovered  by 
Sir  William  Herschel,  who  thought  he  had  discovered  four 
others  also ;  he  may  have  glimpsed  Ariel  and  Umbriel,  but  it 
is  very  doubtful.  They  were  first  certainly  discovered  and 
observed  by  Lassell  in  1851. 

These  satellites,  especially  the  two  inner  ones,  are  telescopi- 
cally  the  smallest  bodies  in  the  solar  system  and  the  hardest  to 
see,  excepting  the  "new"  satellites  of  Jupiter  and  Saturn.  In 
real  size  they  are,  of  course,  much  larger  than  the  satellites  of 
Mars,  very  likely  measuring  from  200  to  500  miles  in  diameter. 

Their  orbits  are  sensibly  circular,  and  all  lie  in  one  plane,  Their  orbits, 
which  ought  to  be,  and  probably  is,  coincident  with  the  plane 
of  the  planet's  equator;  but  the  belts  raise  questions.  They 
are  very  "  close  packed  "  also,  Oberon  having  a  distance  of  only 
375000  miles  and  a  period  of  13d! lh,  while  Ariel  has  a  period 
of  2dllh  at  a  distance  of  120000  miles.  Titania,  the  largest 
and  brightest,  is  at  a  distance  of  280000  miles,  a  little  greater 
than  that  of  the  moon  from  the  earth,  with  a  period  of  8d17h. 

The  most  remarkable  point  about  this  system  remains  to  be 
mentioned.     The  plane  of  their  orbits  is  inclined  82°. 2  to  the  Great  incii 
plane  of  the  ecliptic,  and  in  that  plane  they  revolve  backwards;  natlonof 

J.  the  orbits. 

or  we  may  say,  what  comes  to  the  same  thing,  that  their  orbits  Backward 
are  inclined  to  the  ecliptic  at  an  angle  of  97°. 8,  in  which  case  revolution 

, ,     .  T     . .        .  ,  •  i         i          T  of  satellites. 

their  revolution  is  to  be  considered  as  direct. 


404 


MANUAL   OF   ASTRONOMY 


of  Uranus. 


Minuteness 
of  the  dis- 
crepancy 
between 
theory  and 
observation. 


NEPTUNE 

457.  Discovery  of  Neptune.  —  This  is  reckoned  as  the  greatest 
triumph  of  mathematical  astronomy  since  the  days  of  Newton, 
intractability  It  was  very  soon  found  impossible  to  reconcile  the  old  observa- 
tions of  Uranus  by  Lemonnier  and  others  with  any  orbit  that 
would  fit  the  observations  made  in  the  early  part  of  the  nine- 
teenth century,  and,  what  was  worse,  the  planet  almost  imme- 
diately began  to  deviate  from  the  orbit  computed  from  the  new 
observations,  even  after  allowing  for  the  disturbances  due  to 
Saturn  and  Jupiter.  It  was  misguided  by  some  unknown  influ- 
ence to  an  amount  almost  perceptible  by  the  naked  eye;  the 
difference  between  the  actual  and  computed  places  of  the  planet 
amounted  in  1845  to  the  "intolerable  quantity"  of  nearly  two 
minutes  of  arc. 

This  is  a  little  more  than  one  half  the  distance  between  the  two  prin- 
cipal components  of  the  double-double  star,  e  Lyrae,  the  northern  one  of 
the  two  little  stars  which  form  the  small  equilateral  triangle  with  Vega 
(Fig.  190,  Sec.  585).  A  very  sharp  eye  can  perceive  the  duplicity  of  c 
without  the  aid  of  a  telescope. 

One  might  think  that  such  a  minute  discrepancy  between 
observation  and  theory  was  hardly  worth  minding,  and  that  to 
consider  it  "  intolerable  "  was  putting  the  case  very  strongly, 

De  minimis  but  in  science  unexplained  "  residuals "  are  often  the  seeds 
from  which  new  knowledge  springs.  Just  these  minute  dis- 
crepancies supplied  the  data  which  sufficed  to  determine  the 

Mathemati-    position  of  a  great  world,  before  unknown. 

cai  discovery      Ag  the  regult  of  &  most  skiifui  an(j  laborious  investigation, 

of  Neptune 

byLeverrier.  Leverrier,  a  young  French  astronomer,  wrote  in  substance  to 
Galle,  then  an  assistant  in  the  Observatory  at  Berlin: 

"Direct  your  telescope  to  a  point  on  the  ecliptic  in  the  constella- 
tion of  Aquarius,  in  longitude  326°,  and  you  will  find  within  a 
degree  of  that  place  a  new  planet,  looking  like  a  star  of  about  the 
ninth  magnitude,  and  having  a  perceptible  disk" 


curat 
Seientia. 


THE   MAJOR   PLANETS  405 

The  planet  was  found  at  Berlin  on  the  night  of  Sept.  23,  Optical  dis^ 
1846,  in  exact  accordance  with  this  prediction,  within  half  an 
hour  after  the  astronomers  began  looking  for  it  and  within  52' 
of  the  precise  point  that  Leverrier  had  indicated. 

The  English  Adams  fairly  divides  with  Leverrier  the  honors  for  the    Share  of 
mathematical    discovery    of   the  planet,  having   solved  the  problem   and    Adams  in 
deduced  the  planet's  approximate  place  even  earlier  than  his  competitor. 
The  planet  was  being  searched  for  in  England  at  the  time  when  it  was 
found  in  Germany.     It  had,  in  fact,  been  already  twice  observed,  and  the 
discovery  would  necessarily  have  followed  in  a  few  weeks,  upon  the  reduc- 
tion of  the  English  observations.    The  Berlin  observers  had  the  very  great 
advantage  of  a  new  star  chart  by  Bremiker,  covering  that  very  region  of 
the  sky. 

458.  Error  of  the  Computed  Orbit.  —  Both  Adams  and  Lever-  Error  of 
rier,  besides  calculating  the  planet's  position  in  the  heavens,  c  ^jf™  e 
had  deduced  elements  of  its  orbit  and  a  value  for  its  mass,  to  the 
which  turned  out  to  be  seriously  incorrect.     The  reason  was  assumPtlon 

J  .  of  Bode's 

that  they  assumed  that  the  new  planet's  mean  distance  from  the  Law>  which 
sun  would  follow  Bode's  Law,  a  supposition  quite  warranted  by  here  breaka 
all  the  facts  then  known,  but  which,  nevertheless,  is  not  even 
roughly  true.     As  a  consequence,  their  computed  elements  were 
erroneous,  and  that  to  an  extent  which  has  led  high  authorities 
to  declare  that  the  mathematically  computed  planet  was  not 
Neptune  at  all,  and  that  the  discovery  of  Neptune  itself  was 
simply  a  "  happy  accident." 

This    is    not  so,   however.     While    the    data   and   methods 
employed  were  not  by  themselves  sufficient  to  determine  the 
planet's  orbit  with  accuracy,  they  were  adequate  to  ascertain  Method 
the  planet's  direction  from  the  earth;  the  computers  informed  ^^J68 
the  observers  where  to  point  their  telescopes,  and  this  was  all  direction 
that  was  necessary  for  finding  the  planet.     In  a  similar  case  the  from  earth- 
same  thing  could  be  done  again. 

459.  The  Planet  and  its  Orbit. — The  planet's  mean  distance 
from  the  sun  is  a  little  more  than  2800  000000  miles  (instead  of 


406 


MANUAL   OF   ASTRONOMY 


Data  relat- 
ing to 
planet's 
orbit. 


Telescopic 
appearance 
of  Neptune. 


Diameter  of 
the  planet 
smaller  than 
generally 
accepted 
hitherto. 


Mass  and 
density. 


Albedo  and 
spectrum. 


being  over  3600  000000,  as  it  should  be  according  to  Bode's 
Law).  The  orbit  is  very  nearly  circular,  its  eccentricity  being 
only  0.009.  Even  this,  however,  makes  a  variation  of  over 
50  000000  miles  in  the  planet's  distance  from  the  sun.  The 
period  of  the  planet  is  about  165  years  (instead  of  217,  as  it 
should  be  according  to  Leverrier's  computed  orbit)  and  the 
orbital  velocity  is  about  3£  miles  per  second.  The  inclination 
of  the  orbit  is  about  If  °. 

Neptune  appears  in  the  telescope  as  a  small  star  of  between 
the  eighth  and  ninth  magnitudes,  absolutely  invisible  to  the 
naked  eye,  but  easily  seen  with  a  good  opera-glass,  though  not 
distinguishable  from  a  star  with  a  small  instrument.  Like 
Uranus,  it  shows  a  greenish  disk,  having  an  apparent  diameter, 
according  to  the  measures  of  H.  Struve,  of  2".2.  The  measures 
of  earlier  observers  were  all  much  larger,  and  until  very  recently 
the  value  2".6  was  generally  accepted,  and  is  for  the  present 
allowed  to  stand  in  the  Appendix  tables.  Recent  measures  of 
Struve,  Barnard,  and  See  all  concur,  however,  in  showing  that 
this  value  is  much  too  large. 

Accepting  Struve's  measures,  the  diameter  comes  out  only 
29750  miles,  and  its  volume  fifty-three  times  that  of  the  earth;  but 
the  margin  of  possible  error  must  be  still  quite  large.  The  mass, 
as  determined  from  its  satellite,  is  about  seventeen  times  that  of 
the  earth.  Its  density  (according  to  Struve's  diameter)  comes  out 
0.34,  and  the  surface  gravity  one  and  one-fourth  times  our  own. 

The  planet's  albedo,  according  to  Zollner,  is  0.46,  —  a  trifle 
less  than  that  of  Saturn  and  Venus. 

There  are  no  visible  markings  upon  its  surface,  and  nothing 
certain  is  known  as  to  its'  rotation. 

The  spectrum  of  the  planet  appears  to  be  like  that  of  Uranus, 
but  of  course  is  rather  faint. 

It  will  be  noticed  that  Uranus  and  Neptune  form  a  "pair. of 
twins,"  very  much  as  the  earth  and  Venus  do,  being  almost  alike 
in  magnitude,  density,  and  many  other  characteristics. 


THE   MAJOR   PLANETS  407 

460.  Satellite.  —  Neptune  has  one   satellite,   discovered  by  Neptune's 
Lassell    within   a   month   after    the    discovery  of    the    planet  satelllte* 
itself.     Its  distance  is  about  223000  miles  and  its  period  5d21h. 

Its  orbit  is  inclined  to  the  ecliptic  at  an  angle  of  34°  48'  and  it 
moves  backward  in  it  from  east  to  west,  like  the  satellites  of 
Uranus.  It  is  a  very  small  object,  not  quite  as  bright  as  Oberon, 
the  outer  satellite  of  Uranus.  From  its  brightness,  as  compared 
with  that  of  Neptune  itself,  its  diameter  is  estimated  as  about 
the  same  as  that  of  our  own  moon. 

461.  The  Sun  as  seen  from  Neptune. — At  Neptune's  distance 
the  sun  has  an  apparent  diameter  of  only  a  little  more  than  one 
minute  of  arc,  —  about  the  diameter  of  Venus  when  nearest  us, 
and  too  small  to  be  seen  as  a  disk  by  the  naked  eye,  if  there  be 

eyes  on  Neptune.     The  light  and  heat  there  are  only  -gl^  part  Sunlight  on 
of  what  we  get  at  the  earth.     Still,  we  must  not  imagine  that  NePtune- 
the  Neptunian  sunlight  is  feeble  as  compared  with  starlight, 
or  even  with  moonlight.     At  the  distance  of  Neptune  the  sun 
gives  a  light  nearly  equal  to  700  full  moons,  —  about  eighty 
times  the  light  of  a  standard  candle  at  one  meter's  distance,  — 
and  is  abundant  for  all  visual  purposes.     In  fact,  as  seen  from 
Neptune,  the  sun  would  look  very  like  a  1200  candle-power 
electric  arc  at  a  distance  of  only  12  or  13  feet. 

462.  Ultra-Neptunian  Planets.  —  Perhaps  the  breaking  down  Possible 
of   Bode's   Law  at  Neptune  may  be  regarded  as  an  indication  Planet^ 
that  the  solar  system  ends  there,  and  that  there  is  no  remoter  Neptune, 
planet ;  but  of  course  it  does  not  make  it  certain.     If  such  a 
planet  of  any  magnitude  exists,  it  is  sure  to  be  found  sooner  or     • 
later,  probably  by  means  of  the  disturbances  it  produces  in  the 
motion  of  Uranus   and  Neptune.    Professor  W.  H.  Pickering 

has  recently  determined  the  elements  of  such  a  hypothetical 
planet  "  O,"  basing  his  determination  upon  the  perturbations 
of  Uranus.  A  photographic  search  for  the  planet  is  now  in 
progress. 


408  MANUAL   OF   ASTRONOMY 


EXERCISES 

1.  When  Jupiter  is  visible  in  the  evening  do  the  shadows  of  his  satel- 
lites precede  or  follow  the  satellites  as  they  cross  the  planet's  disk  ? 

2.  On  which  limb,  the  eastern  or  the  western,  do  the  satellites  appear 
to  enter  upon  the  disk  ? 

3.  What  probable  effect  would  the  great  mass  of  Jupiter  have  upon 
the  size  of  animals  inhabiting  it,  if  there  were  any  ? 

4.  How  would  sunlight   upon   Saturn   compare  with  sunlight  on  the 
earth  ?     How  with  moonlight  ? 

5.  What  would  be  the  greatest  elongation  of  the  earth  from  the  sun  as 
seen  from  Jupiter  ?  from  Saturn  ?  from  Uranus  ? 

G.  What  would  be  the  apparent  angular  diameter  of  the  earth  when 
"  transiting  "  the  sun  as  seen  from  Jupiter  ? 

7.  What  is  the  rate  in  miles  per  hour  at  which  a  white  spot  on  the 
equator  of  Jupiter,  showing  a  rotation  period  of  9h50m,  would  pass  a  dark 
spot  indicating  a  period  of  9h55m? 

8.  Find  the  diameter,  volume,  density,  and  surface  gravity  of  Neptune, 
accepting  See's  measured  diameter  of  the  planet,  viz.,  2".01,  taking  the 
planet's  mass  as  17  times  that  of  the  earth,  the  solar  parallax  as  8".80, 
and  the  mean  distance  of  Neptune  from  the  sun  as  30.055. 

(  Diameter,  27200  miles. 
Ans.  \  Volume,  41  times  the  earth. 
[Density,  0.42. 

NOTE  TO  SECS.   438  AND  452 

THE  NEW  SATELLITES.  The  sixth  and  seventh  satellites  of  Jupiter  were 
discovered  in  January  and  February,  1905,  by  Perrine,  at  the  Lick  Observatory, 
on  photographs  made  with  the  Crossley  reflector.  They  are  both  extremely 
small, — the  seventh  the  smaller, — and  probably  beyond  the  reach  of  visual 
observation.  They  are  far  outside  the  region  of  the  older  satellites, — a  pair 
of  twins  with  orbits  of  nearly  the  same  size,  more  than  seven  million  miles  in 
radius,  inclined  about  30°  to  the  plane  of  the  planet's  equator  and  to  each  other. 
The  eighth  satellite  was  discovered  by  Melotte  in  1908  on  photographs  made  at 
Greenwich  for  the  sixth  and  seventh.  Its  distance  from  Jupiter  is  more  than 
twice  as  great  (16  000000  miles),  and  its  motion,  like  that  of  Saturn's  ninth  sat- 
ellite, is  retrograde. 

Themis,  Saturn's  tenth  satellite,  was  found  by  Pickering  in  April,  1905,  upon 
nine  of  the  plates  which  had  been  used  in  the  investigation  of  Phoebe.  She  is  a 
little  twin  sister  of  Hyperion,  but  is  three  magnitudes  fainter,  and  has  an  orbit 
of  almost  the  same  size  and  period,  though  more  eccentric  and  differently  tilted. 
The  data  of  Table  II  are  only  provisional. 


CHAPTER   XV 

METHODS    OF   DETERMINING   THE    PARALLAX   AND 
DISTANCE    OF  THE    SUN 

Importance  and  Difficulty  of  the  Problem  —  Historical  —  Classification  of  Methods 
—  Geometrical  Methods  —  Oppositions  of  Mars  and  Certain  Asteroids,  and  Tran- 
sits of  Venus  —  Gravitational  Methods 

463,  In  some  respects  the  problem  of  the  sun's  distance  is  the 
most  fundamental  of  all  that  are  encountered  by  the  astron- 
omer. It  is  true  that  many  important  astronomical  facts  can 
be  ascertained  before  it  is  solved  :  for  instance,  by  a  method 
which  has  been  given  in  Sec.  371,  we  can  determine  the  rela-  Relative 
tive  distances  of  the  planets  and  form  a  map  of  the  solar  svstem,  distances  in 

.  ,      ,  solar  system 

correct  in  all  its  proportions,  although  the  unit  of  measurement  easily  deter- 
is  still  undetermined,  —  a  map  without  any  scale  of  miles.     But  mined- 
to  give  the  map  its  use  and  meaning,  we  must  ascertain   the 
scale,  and  until  we  do  this  we  can  have  no  true  conception  of 
the   real  dimensions,  masses,   and    distances    of   the   heavenly 
bodies  as  compared  with  our  terrestrial  units  of  mass  and  dis- 
tance.    Any  error  in  the  assumed  value  of  the   astronomical 
unit  propagates  itself  proportionally  through  the  whole  system, 
not  only  solar  but  stellar. 

The  difficulty  of  the  problem  equals  its  importance.     It  is  no  importance 
easy  matter,  confined  as  we  are  to  our  little  earth,  to  reach  out  and  diffi" 
into  space  and  stretch  a  tape-line  to  the  sun.     In  Sees.  173  and  determining 
442  we  have  already  given  the  two  methods  of  determining  the  absolute 
sun's  distance,  which  depend  on  our  experimental  knowledge 
of  the  velocity  of  light.     They  are  satisfactory  and  sufficient 
for  the  purposes  of  the  text.     But  methods  of  this  kind  have 
become  available  only  since  1849. 

409 


410  MANUAL   OF  ASTRONOMY 

Previously  astronomers  were  confined  entirely  to  purely 
astronomical  methods,  depending  either  upon  geometrical  meas- 
urement of  the  distance  of  one  of  the  nearer  planets  when 
favorably  situated,  or  else  upon  certain  gravitational  relations 
which  connect  the  distance  of  the  sun  with  some  of  the  irregu- 
lar motions  of  the  moon,  or  with  the  earth's  power  of  disturbing 
her  neighboring  planets,  Venus  and  Mars. 

Solar  par-          464.    Historical.  —  Until  nearly  1700  no  even  approximately 
aiiaxS',         accurate  knowledge  of  the  sun's  distance  had  been  obtained. 

according  to 

Ptolemy.        Up  to  the  time  of  Tycho  it  was  assumed  on  the  authority  of 

Ptolemy,  who  rested  on  the  authority  of  Hipparchus,  who  in 

his  turn  depended  upon  an  observation  of  Aristarchus  (erroneous, 

though  ingenious  in  its  conception),  that  the  sun's  horizontal 

parallax  is  3',  —  a  value  more  than  twenty  times  too  great. 

Proof  that          Kepler,  from  Tycho's  observations  of  Mars,  satisfied  himself 

this  must  be  fa^  ^he  parallax  certainly  could  not  exceed  1',  and  was  prob- 

by Kepler      ably  much  smaller;  and  at  last,  about  1670,  Cassini  also,  by 

and  Cassini.  means  of  observations  of  Mars  made  simultaneously  in  France 

and  South  America,  showed  that  the  solar  parallax  could  not 

exceed  10". 

Value  The  transits  of  Venus  in  1761  and  1769  furnished  data  that 

approxi-        proved  it  to  lie  between  8"  and  9",  and  the  discussion  of  all  the 
correct          available  observations,  published  by  Encke  about  1824,  gave  as 
obtained        a  result  8".5776,  corresponding  to  a  distance  of  about  95  000000 
of  Venus  in    miles.     The  accuracy  of  this  determination  was,  however,  by  no 
1761  and        means  commensurate  with  the  length  of  the  decimal,  and  its 
error  began  to  be  obvious  about  1860.     It  is  now  practically 
settled  that  the  true  value  lies  somewhere  between  8". 75  and 
8".85,  the  sun's  mean  distance  being  between  92  400000  and 
93  500000  miles.     Indeed,  it  is  now  certain  that  the  figure  8". 8, 
adopted  in  the  text,  must  be  extremely  near  the  truth, 
ciassifica-          The   methods  available  for  determining  the  distance  of  the 
m°th°fd          sun  may  ^e  classined  under  three  heads,  — geometrical,  gravita- 
tional, and  physical.     The  physical  methods  (by  means  of  the 


METHODS  OF  DETERMINING  THE  PARALLAX   411 

velocity  of  light)  have  been  already  discussed  (Sees.  173  and 
442 ;  see  also  note  to  Sec.  542).  We  present  briefly  the  prin- 
cipal methods  which  belong  to  the  two  other  classes. 

GEOMETEICAL   METHODS 

465.  The  direct  geometrical  method  of  determining  the  sun's  Direct 
distance  and  parallax  (by  observing  the  sun  itself  at  stations  geometrical 
widely  separated  on  the  earth,  in  the  same  way  that  the  dis-  useless, 
tance  of  the  moon  is  found  —  Sec.  196)  is  practically  worthless. 

The  parallax  of  the  sun  being  only  8". 8,  the  inevitable  errors  of 
the  best  direct  observation  would  be  far  too  large  a  fraction 
of  the  quantity  sought.  Moreover,  the  sun,  on  account  of  the 
effect  of  its  heat  upon  an  instrument,  is  a  very  unsatisfactory 
object  to  observe. 

Since,  however,  we  can  compute  at  any  time  the  distance  of  any 
planet  from  the  earth  in  astronomical  units,  it  will  answer  every 
purpose  to  measure  the  distance  in  miles  to  any  one  of  them. 

466.  Observations  of  Mars.  —  When  Mars  comes  nearest  to  indirect 

the  earth  its  distance  from  us  can  be  measured  with  reasonable  determina- 

• ,  i         <.  ,  tion  by 

accuracy  in  either  of  two  ways :  observa- 

(1)  By  observations  from  two  or  more  stations  widely  separated  tions  of 

•      7    , . ,     7  Mars ;  two 

in  latitude.  meth<;ds> 

(2)  By  observations  of  the  planet  from  a  single  station  near 
the  equator  when  the  planet  is  near  its  rising  and  setting. 

In  the  first  case  the  observations  may  be  (a)  meridian-circle 
observations   of  the  planet's  zenith-distance,   exactly  such   as 
are  used  for  getting  the  distance  of  the  moon  (Sec.  196);  or 
(b)  they  may  be  micrometer  or  heliometer  measures  of  the  differ-  First 
ence  of  declination  between  the  planet  and  stars  near  it;  or,  method 
finally,   (c)  instead  of  measuring  this  distance  directly  photo-  able  in 
graphs  may  be  taken  and  measured  later.  requiring 

Since,  however,   at   least   two   different  observers  and  two  servers"  and 
different  instruments  are   concerned  in  the   observations,  the  instruments. 


412 


MANUAL   OF   ASTRONOMY 


results  are  less  trustworthy  than  those  obtained  by  the  second 
method. 

467.    In  this  case  a  single  observer,  by  measuring  (best  with  a 
heliometer — Sec.  72)  the  apparent  distance  between  the  planet 
and  small  stars  nearly  east  and  west  of  it  at  the  times  when  the 
planet  is  near  the  horizon,  can  determine  its  par- 
allax with  great  accuracy. 

Fig.  153  illustrates  the  principle  involved. 
When  the  observer  at  A  (a  point  on  or  near  the 
earth's  equator)  sees  the  planet  M  just  rising,  he 
sees  it  at  a  (a  point  on  the  celestial  sphere  east 
of  0,  the  point  where  it  would  be  seen  from 
the  center  of  the  earth),  the  angle  CM  A  being 
the  planet's  equatorial  horizontal  parallax. 

Twelve  hours  later,  when  the  rotation  of  the 
earth  has  taken  the  observer  to  B  and  the  planet 
is  setting,  he  sees  it  at  5,  displaced  by  parallax 
just  as  much  as  before,  but  to  the  west  of  <?,  its 
geocentric  place.  In  other  words,  when  the 
planet  is  rising  the  parallax  increases  its  right 
ascension,  and  when  setting  diminishes  it. 

Suppose,  now,  that  for  the  moment  the  orbital 
motion  of  the  planet  and  the  earth  are  suspended, 
the  planet  being  at  opposition  and  as  near  the 
FIG.  153         earth  as  possible.     If,  then,  when  the  planet  is 
rising  we   measure  the   apparent  distance,   MeS 
(Fig.  154),  from  a  star,   S,  and  twelve  hours  later  measure  it 
again,  the  distance  Me  to  Mw  will  be  twice  the  horizontal  paral- 
lax of  the  planet.     The  earth's  rotation  will  have  carried  the 
observer  a  long  journey,  transporting  him  and  his  instrument, 
without  disturbance,  expense,  or  trouble,  to  a  (virtually)  different 
station  8000  miles  away. 

In  practice  the  observations,  of  course,  cannot  be  made  at  the 
moment  when  the  planet  is  exactly  on  the  horizon,  but  they  are 


METHODS   OF   DETERMINING   THE   PARALLAX       413 


kept  up  during  the  whole  time  while  the  planet  is  crossing  the 
heavens.  Moreover,  measures  are  made  not  from  one  star 
only,  but  from  all  that  are  in  the  planet's  neighborhood.  The 
orbital  motion,  both  of  the  planet  and  of  the  earth,  during  the 
observations  must  also  be  allowed  for;  but  this  presents  no 
serious  difficulty. 

The  most  important  application  of  this  method  was  in  1877, 
at  Ascension  Island,  by  Gill  (now  Sir  David  Gill  of  the  Cape 
of  Good  Hope  Observatory).  He  got  for  the  solar  parallax 
8".783  ±  .015.  The  size  of  the  planet's  disk,  its  brightness, 
and  its  "phase"  (except  at  the 
moment  of  opposition),  however, 
interfere  somewhat  with  the  pre- 
cision of  the  necessary  measure- 
ments, and  the  great  difference 
of  brightness  between  it  and  the 
stars  makes  it  difficult  to  use 
photography. 

468.  Observations  of  Asteroids. 
—  The  asteroids  do  not  present 
the  same  difficulties  in  determin- 
ing their  apparent  places  among 
the  stars  by  heliometer  measures 
or  photography,  since  they  them- 
selves are  mere  starlike  points. 
Although  none  of  them  (except 

Eros)  come  quite  as  near  to  the  earth  as  Mars,  several  of  them 
come  near  enough  to  make  it  possible  to  obtain  from  their 
observations  results  notably  more  satisfactory  than  those  from 
Mars. 

The  heliometer  observations  of  Iris,  Sappho,  and  Victoria, 
made  by  Gill  at  the  Cape  of  Good  Hope  in  1889-91,  in  concert 
with  several  other  heliometer  observers  in  Europe  and  America, 
gave  8".802  ±  .005.  In  this  case,  of  course,  the  method  used 


Observa- 
tions of 
Gill  at 
Ascension 
Island. 


G 

M 

S2        p' 

Me 

2V 

•s 

Parallax 

1, 

*- 

by  observa- 

s      "s* 

tions  of 

asteroids. 

\ 

FIG.  154.  —  Micrometric  Comparison 
of  Mars  with  Neighboring  Stars 


414 


MANUAL   OF   ASTRONOMY 


Eros 

observed  in 
1900-01. 


Transits  of 
Venus:  her 
displace- 
ment on 
sun's  disk  is 
2.61  times 
her  parallax. 


General 
principle  by 
which  solar 


was  neither  (1)  nor  (2)  of  Sec.  466  exclusively.  The  apparent 
displacements  of  the  planets,  due  both  to  the  distance  between 
the  stations  and  to  the  motion  of  the  stations  on  the  whirling 
earth,  all  contribute  to  the  result,  complicating  the  calculation, 
but  increasing  its  precision. 

We  have  already  spoken  of  the  case  of  Eros  (Sec.  427).  The 
observations  of  1900-01,  largely  photographic,  ought,  when  they 
have  been  thoroughly  discussed,Ho  give  a  result  even  more  pre- 
cise than  that  last  quoted.  In  1931,  if  the  weather  is  good  for 
a  few  days  at  the  critical  time  when  the  planet  is  nearest,  the 
opportunity  will  be  still  more  favorable. 

469.  Transits  of  Venus.  —  When  Venus  is  at  or  near  inferior 
conjunction  her  distance  is  less  than  that  of  Mars  at  opposi- 
tion ;  but  she  cannot  be  observed  for  parallax  in  the  same  way, 
because  she  is  then  in  the  twilight,  and  little  stars  near  her 
cannot  be  seen  for  use  as  reference  points.  Now  and  then, 
however,  she  passes  between  us  and  the  sun  and  "  transits " 
the  disk,  as  explained  in  Sec.  405.  Her  distance  from  the 

earth  is  then  only  26  000000  miles, 
and  her  parallax  is  much  greater 
than  that  of  the  sun.  Seen  by  two 
observers  at  different  stations  on  the 
earth,  she  will  therefore  appear  to  be 
projected  on  two  different  points  of 
the  sun's  disk,  and  her  apparent  angu- 
lar displacement  on  the  sun's  surface 
will  be  the  difference  between  her 
own  parallactic  displacement  (corre- 
sponding to  the  distance  between  the 

two  stations)  and  that  of  the  sun  itself.  This  relative  displace- 
ment is  Hf,  or  2.61,  times  as  great  as  the  displacement  of 
the  sun. 

To  determine  the  solar  parallax,  then,  by  means  of  the  tran- 
sit of  Venus,  we  must  somehow  measure  the  apparent  distance 
1  See  note  on  page  378. 


FIG.  155.  —  Contacts  in  a  Transit 
of  Venus 


METHODS  OF  DETERMINING  THE  PARALLAX   415 

in  seconds  of  arc  between  two  positions  of  Venus  on  the  sun's  parallax  is 
disk,  as  seen  simultaneously  from  two  widely  distant  stations  determmed 

J  from  transit. 

of  known  latitude  and  longitude  on  the  earth  s  surface. 

The  methods  earliest  proposed  and  executed  depend  upon  Methods 
observations  of  the  instant  of  contact  between  the  planet  and  dePeinding 

on  observa- 

the  sun's  limb.     There  are  four  of  these  contacts,  as  shown  in  tions  of  the 
Fig.  155,  the  first  and  fourth  external,  the  second  and  third  contacts- 
internal. 

470.   Haiiey's  Method,  or  the  Method  of  Durations.  —  Halley  Haiiey's 
was  the  first  to  notice,  in  1679,  the  peculiar  advantages  of  the  method: 

.    .  ,  durations 

transit  of  Venus  as  a  means  tor  determining  the  distance  of  observed 

the  sun,  and  he  proposed  a  method  which  consists  in  simply  from 

observing  the  duration  of  the  transit  at  stations  chosen  as  far  far  apart  }n 

apart  in  latitude  as  possible.  latitude. 

This  had  the  great  advantage  of  not  requiring  an  accurate  Advantages 

knowledge  of  the  longitudes  of  the  stations,  which  in  his  time  and  dlsad- 

vantages. 

would  have  been  very  difficult  to  determine,  nor  did  it  require 

_=== \f 

v  -J^~ 

(Earth) 


FIG.  156.  — Haiiey's  Method 

any  knowledge  of  the  absolute,  or  Greenwich,  time  of  contact. 
It  is  only  necessary  to  know  the  latitudes  of  the  observers 
and  that  their  timepieces  should  run  accurately  during  the  short 
time  (five  or  six  hours)  while  the  planet  is  crossing  the  sun's  disk. 
On  the  other  hand,  the  stations  must  be  in  high  latitudes,  and 
the  observer  must  see  both  beginning  and  end  of  the  transit ;  if 
he  loses  either  on  account  of  clouds,  the  method  fails. 

Fig.  156  illustrates  in  a  general  way  the  principle  involved: 
the  two  observers  at  E  and  B  see  the  planet  crossing  the  sun's 
disk  on  the  chords  df  and  ac,  respectively,  and  from  the  duration 


416 


MANUAL   OF    ASTRONOMY 


and  known  rate  of  motion  of  the  planet  the  length  of  the  two 
chords  in  seconds  of  arc  can  be  computed  with  more  accuracy 
than  it  can  be  determined  by  any  micrometer  measure,  provided 
the  instant  of  contact  can  be  accurately  observed.  But,  since  the 
angular  semidiameter  of  the  sun  is  known,  the  distances  bS  and 
eS  of  the  two  chords  from  the  center  of  the  sun  can  be  com- 
puted, and  their  difference,  eb  (all  in  seconds  of  arc),  and  that 
with  very  great  accuracy  if  the  chords  fall,  as  they  have  done  in 
all  the  transits  yet  observed,  near  the  edge  of  the  sun's  disk. 

But,  since  VE  and  Ve  are  in  the  proportion  of  277  to  723, 
eb  (in  miles)  is  J|-|-  of  EB,  provided  the  two  stations  are  so 
chosen  that  the  line  EB  is  perpendicular  to  the  plane  of  the 
planet's  orbit  (if  not,  due  allowance  must,  and  can,  be  made  to 
get  the  "effective  length"  of  EB). 

We  have,  then,  eb,  both  in  seconds  and  in  miles;  we  know, 
therefore,  how  many  miles  go  to  one  second  of  arc  at  the  sun's 
distance.  It  comes  out  about  450,  and  therefore  (Sec.  10,  eb 
taking  the  place  of  r)  the  sun's  distance  is  about  450  miles  X 
206265,  or  92  800000  miles. 

For  details  of  the  methods  of  accurate  calculation  from  the 
actual  observations,  the  reader  must  be  referred  to  works  deal- 
ing with  the  special  subject. 

Halley  expected  to  depend  mainly  on  the  twTo  internal  con- 
tacts, which  he  supposed  could  be  observed  with  an  error  not 
exceeding  a  single  second  of  time.  If  so,  the  observations 
would  determine  the  sun's  parallax  within  g-J--^  of  its  true  value. 

Unfortunately,  this  accuracy  is  not  found  practicable.  There 
are  usually  large  errors  caused  by  the  imperfection  of  the  tele- 
scope and  eye  of  the  observer,  as  well  as  atmospheric  condi- 
tions. And  even  if  these  are  avoided,  the  atmosphere  of  the 
planet  introduces  a  difficulty  that  cannot  be  evaded;  it  pro- 
duces a  luminous  ring  around  the  edge  of  the  planet  (Sec.  401, 
Fig.  137),  which  prevents  any  certainty  as  to  the  precise  moment 
when  the  planet's  disk  is  tangent  to  the  limb  of  the  sun.  The 


METHODS   OF   DETERMINING   THE   PARALLAX       417 

contact  observations  during  the  last  two  transits  in  1874  and 
1882  were  uncertain,  under  the  very  best  conditions,  by  at  least 
five  or  six  seconds. 

471.   Deiisie's  Method.  —  Halley's  method  requires  stations  in  Deiisie's 
high  latitudes,  uncomfortable  and  hard  to  reach,  and  so  chosen  ™ethod: 

observa- 

that  both  the  beginning  and  end  can  be  seen.     And  both  must  tions  of 
be  seen  or  the  method  fails.  absolute 

Deiisie's  method,  on  the  other  hand,  employs  pairs  of  stations  contact  from 
near  the  equator,  but  as  nearly  as  possible  on  opposite  sides  of  equatorial 
the  earth,  and  it  does  not  require  that  the  observer  should  see 


both  the  beginning  and  end  of  the  transit,  —  observations  of  separated. 
either  phase  can  be  utilized  for  their  full  value,  which  is  a  great 


FIG.  157.  —  Deiisie's  Method 

advantage,  —  but  it  requires  that  the  longitudes  of  the  stations 
should  be  known  with  extreme  precision,  since  the  method  con- 
sists essentially  in  observing  the  absolute  time  of  contact  (i.e., 
Greenwich  or  Paris  time  at  both  stations).  It  is  beautifully 
simple  and  easy  to  understand. 

An  observer  at  E  on  the  equator  (Fig.  157)  on  one  side  of 
the  earth  notes  the  moment  of  internal  contact  in  Greenwich 
time,  the  planet  being  then  at  V^ ;  when  W,  on  the  other  side  of 
the  earth,  notes  the  contact  (also  in  Greenwich  time)  the  planet 
will  be  at  F2,  and  the  angle  V\DV%  is  the  earth's  apparent 
diameter  as  seen  from  the  sun,  i.e.,  twice  the  sun's  horizontal  Theoretical 
parallax  (Sec.  78).  Now  the  angle  at  D  is  at  once  determined  simplicity  of 

*  the  method. 

by  the  time  occupied  by  Venus  in  moving  from  Vl  to  F"2.  It  is 
simply  just  the  same  fraction  of  360°  that  this  elapsed  time  is  of 
684  days,  the  planet's  synodic  period.  If,  for  example,  the 


418 


MANUAL   OF   ASTRONOMY 


difference  of  time  were  eleven  and  a  half  minutes  between  the 
contact  as  observed  at  E  and  W,  we  should  find  the  angle  at  D 
to  be  about  11". ,7. 

From  all  the  contact  observations,  several  hundred  in  number, 
made  during  the  transits  of  1874  and  1882,  Newcomb  gets  a 
solar  parallax  of  8".794  ±  .018. 

472,  Heliometric  and  Photographic  Observations. — Instead  of 
observing  merely  the  four  contacts  and  leaving  the  rest  of  the 
photometric  transit  unutilized,  we  may  either  keep  up  a  continued  series  of 
measurements  of  the  planet's  position  upon  the  sun's  disk  with 
a  heliometer,  or  we  may  take  a  series  of  photographs  to  be 
measured  up  at  leisure.  Such  heliometer  measures  or  photo- 
graphs, taken  in  connection  with  the  recorded  Greenwich  times 
at  which  they  were  made,  furnish  the  means  of  determining 
just  where  the  planet  appeared  to  be  on  the  sun's  disk  at  any 
given  moment,  as  seen  from  the  observer's  station.  A  compari- 
son of  these  positions  with  those  simultaneously  occupied  by 
the  planet,  as  seen  from  another  station,  gives  at  once  the  means 
of  deducing  the  parallax. 

In  1874  and  1882  several  hundred  heliometer  measures  were 
made  (mostly  by  German  parties),  and  about  six  thousand 
photographs  were  obtained  at  stations  in  all  quarters  of  the 
earth  where  the  transits  could  be  seen,  —  more  than  two  thou- 
sand by  the  different  American  parties.  The  final  result  of 
all  these  observations  is  given  by  Newcomb  as  8". 857  ±  .023,  — 
differing  to  an  unexpected  degree  from  the  figures  given  by 
other  methods,  and  seriously  discordant  among  themselves,  as 
shown  by  the  large  probable  error. 

It  looks  as  if  measurements  of  this  sort  must  be  vitiated  by  some  con- 
stant source  of  error  as  yet  undetected. 

On  the  whole,  the  outcome  of  the  two  transits  has  been  to  satisfy 
astronomers  that  other  methods  of  determining  the  sun's  parallax  are  to 
be  preferred,  as  Leverrier  maintained  in  1870.  It  is  hardly  likely  that 
transits  will  ever  again  be  observed  so  elaborately  and  expensively. 


METHODS   OF   DETERMINING   THE   PARALLAX       419 


473.   Gravitational  Methods.  —  The  scope  of  our  work  makes  Gravita- 
tional 

methods. 


it  impossible  to  give  any  more  than  a  very  elementary  explana-  t 


tion  of  the  principles  involved,  since  the  details  of  investiga- 
tion belong  to  a  higher  range.  Of  the  different  methods  of  this 
class  we  mention  two  only: 

(1)  By  the  moon's  parallactic  inequality,  so  called  because  by  By  parai- 
it  the  sun'sr  parallax  can  be  determined.  lactic  in- 

It  depends  upon  the  fact  that  the  sun's  disturbing  effect  upon  the  moon! 
the  moon  is  sensibly  greater  in  the  half  of  the  moon's  orbit 
nearest  the  sun  (i.e.,  the-  quarter  on  each  side  of  new  moon)  than 
it  is  in  the  remoter  half; "and  the  difference  depends  upon  the 
ratio  between  the  radius  of  the  moon's  orbit  around  the  earth  to  that 
of  the  earth's  orbit  around  the  sun.  If  that  ratio  can  be  deter- 
mined, the  radius  of  the  earth's  orbit  comes  out  in  terms  of  the 
distance  of  the  moon  from  the  earth,  which  is  accurately  known. 

As  a  consequence  of  this  difference  of  the  sun's  disturbing 
force  on  the  two  halves  of  the  orbit,  the  moon  at  the  end  of  the 
first  quarter  is  about  two  minutes  of  arc  (120")  behind  the 
place  she  would  occupy  if  there  were  no  such  inequality  in 
the  disturbing  force.  At  the  third  quarter  (a  week  after  full 
moon)  she  is  as  much  ahead. 

If  the  moon's  place  could  be  observed  as  accurately  as  that  of  a  star, 
this  method  would  stand  extremely  high  for  precision ;  but  the  observa- 
tional difficulties  are  serious,  and  the  difficulty  is  much  increased  by  the 
fact  that  at  the  first  quarter  we  are  obliged  to  observe  the  western  limb  of 
the  moon,  and  at  the  third  the  eastern.  Still,  the  result  obtained  from  it 
agrees  very  well  with  that  from  the  other  methods. 

474 (2)  The  second  method  is  by  the  perturbations  produced  By  pertur- 

by  the  earth  on  the  orbits  of  Venus  and  Mars  (and  we  may  now  bationsPr°- 
add  Eros).     The  method  depends  upon  the  principle  that  the  the  earth, 
amount  of  these  perturbations  depends  upon  the  ratio  of  the 
mass  of  the  earth  (including  the  moon)  to  that  of  the  sun;  and, 
further,  that  when  this  ratio  of  masses  is  known  the  distance  '•*> 
of  the  sun  follows  at  once  from  a  simple  equation,  easily  deduced. 


420 


MANUAL   OF   ASTRONOMY 


From  Sec.  381,  equation  (1),  we  have,  changing  a  few  letters 
(putting  (S  +  E)  for  (M+  m)  and  D  for  r), 


Deduction 
of  parallax 
from  the 
ratio 
between 
the  masses 
of  earth 
and  sun. 


Advantages 
of  the  gravi- 

tational 

method. 
its  precision 


in  which  S  and  E  are  the  masses  of  the  sun  and  earth,  G  is  the 
constant  of  gravitation,  D  is  the  mean  distance  of  the  earth 
from  the  sun,  and  T  the  number  of  seconds  in  a  year. 

Also,  for  the  force  of  gravity  at  the  earth's  surface,  we  have 

g  =  G  x  -« i  whence  E  =  —  x  ^  f  being  the  radius  of  the  earth. 
Dividing  the  preceding  equation  by  this,  we  get 
8  +  E      4  7T2  A 


E 


whence, 


If  we  put  —  =  Jf,  this  becomes  D3  =  (     .          )#T2r2,  in  which 
E  \  4  ?H  y  ' 

everything  is  known  if  M  is  determined,  g  being  given  by  pen- 
dulum observations  and  r  by  measurements  of  the  earth's 
dimensions,  while  T  is  the  length  of  the  sidereal  year  in  seconds. 

The  matter  can  also  be  treated  differently,  bringing  out  the 
sun's  distance  in  terms  of  the  distance  and  period  of  the  moon, 
instead  of  g  and  r. 

The  great  beauty  of  the  gravitational  method  lies  in  this,  — 
^at  ag  ^.-  me  _oeg  on  an(j  ^he  effects  of  the  earth  upon  the  nodes 
and  apsides  of  the  neighboring  orbits  accumulate,  the  determina- 
fton  of  t^e  earth's  mass  in  terms  of  the  sun's  becomes  continually 
and  cumulatively  more  precise.  Even  at  present  the  method 
ranks  high  for  accuracy,  —  so  high  that  Leverrier,  who  first 
developed  it,  would,  as  already  mentioned,  have  nothing  to  do 
with  the  transit-of-Venus  observations  in  1874,  declaring  that 
all  such  old-fashioned  ways  are  absolutely  valueless.  By  this 
method  Newcomb  deduces  a  parallax  of  8".768  ±  0".010. 


METHODS    OF   DETERMINING   THE    PARALLAX       421 
475.    It  is  to  be  noticed  that  the  geometrical  methods   give  Accordance 


the  parallax  of  the  sun  directly,  apart  from  all  hypothesis  or  b 

assumption,  except  as  to  the  accuracy  of  the  observations  them-  the  different 
selves,  and  of  their  necessary  corrections  for  refraction,  etc.    The  metnods- 
gravitational  methods,  on  the  other  hand,  assume  the  exactness 
of  the  law  of  gravitation  ;  and   the  physical  method  (by  the 
velocity  of  light)  assumes  that  light  travels  in  space  with  the 
same  velocity  as  in  our  terrestrial  experiments,  after  allowing 
for  the  retardation  due  to  the  refracting  power  of  the  air.     The 
near  accordance  of  the  results  obtained  by  the  different  methods 
shows  that  these  assumptions  must  be  very  nearly  correct,  though 
perhaps  not  absolutely  so. 

We  add  a  little  table  giving  the  distance  of  the  sun  corre-  Distance  of 
spending  to  different  values  of  the  solar  parallax,  assuming  the  sun  corre" 
equatorial  radius  of  the  earth  to  be  3963.3  miles.  different 

8".75  corresponds  to  23573  equatorial  radii  of  the  earth  =  93  428000  miles. 
8".80  «  »  23439          «  "      "    «       «      =  92  897000     " 

8".85  «  «  23307          «  «      «    «       «      =  92  372000     » 

Newcomb,  in  his  Astronomical  Constants  (1896)  adopts  8".  797 
±0n.007  as  the  value  of  the  solar  parallax  to  be  used  in  the 
planetary  tables  of  the  American  ephemeris. 

He  also  gives  the  following  as  the  results  derived  by  the  various  methods   Newcomb's 
after  making  allowance  for  probable  systematic  errors,  and  assigns  to  each    summary 

result  the  weight  indicated  by  the  number  that  follows  it.  of  Parallax 

J  results. 

Motion  of  the  Node  of  Venus  ........  8".768,  10 

GUI's  Observations  of  Mars  (1877)     ......  8  .780,  1 

Pulkowa  Constant  of  Aberration  (20".492)      ...  8  .793,  40 

Contact  Observations  of  Transit  of  Venus  ....  8  .794,  3 

Heliometer  Observations  of  Victoria  and  Sappho    .     .  8  .799,  5 

Parallactic  Inequality  of  the  Moon     ......  8  .794,  10 

Miscellaneous  Determinations  of  Aberration  (20"  A63)  8  .806,  10 

Lunar  Inequality  of  the  Earth       .......  8  .818,  1 

Measures  of  Venus  in  Transit  ........  8  .857,  1 

Harkness,  in  his  Solar  Parallax  and  its  Related  Constants 
(1891),  obtained  as  his  final  value  8".809  ±  0".006. 


CHAPTER  XVI 


General 
appearance 
of  comets. 


Their 
number. 


COMETS 

Their  Number,  Designation,  and  Orbits  —  Their  Constituent  Parts  and  Appearance— 
Their  Spectra  —  Physical  Constitution  and  Behavior  —  Danger  from  Comets 

476.  The  comets  are  bodies  very  different  from  the  stars  and 
planets.    They  appear  from  time  to  time  in  the  heavens,  remain 
visible  for  some  weeks  or  months,  pursue  a  longer  or  shorter 
path,  and  then  fade  away  in  the  distance.      They  are  called 
comets  (from  coma,  i.e.,  "hair"),  because  when  one  of  them  is 
bright  enough  to  be  seen  by  the  naked  eye  it  looks  like  a  star 
surrounded  by  a  luminous  fog  and  usually  carries  with  it  a 
long  stream  of  hazy  light. 

Large  comets  are  magnificent  objects,  sometimes  as  bright 
as  Venus  and  visible  by  day,  with  a  dazzling  nucleus  and  a 
nebulous  head  as  large  as  the  moon,  accompanied  by  a  train 
which  extends  half-way  from  the  horizon  to  the  zenith,  and 
sometimes  is  really  long  enough  to  reach  from  the  earth  to  the 
sun.  Such  are  rare,  however  ;  the  majority  are  faint  wisps  of 
light,  visible  only  with  the  telescope. 

Fig.  158  is  a  representation  of  Donati's  comet  of  1858,  one 
of  the  finest  ever  seen. 

In  ancient  times  comets  were  always  regarded  with  terror,  either  as 
actually  exerting  malignant  influences,  or  at  least  ominous  of  evil,  and  the 
notion  still  survives  in  certain  quarters,  although  the  most  careful  research 
fails  to  show,  or  even  suggest,  the  slightest  reason  for  it. 

477.  Number  of  Comets.  —  Thus  far,  up  to  the  beginning  of 
the  new  century,  our  lists  contain  nearly  eight  hundred,  about 
four  hundred  of  which  were  observed  before  the  invention  of 

422 


COMETS  423 


the  telescope  in  1609,  and  therefore  must  have  been  bright.     Of 
those  observed  since  then,  only  a  small  proportion  have  been 


FIG.  158.  —  Naked-Eye  View  of  Donati's  Comet,  Oct.  4,  1858 
Bond 

conspicuous  to  the  naked  eye,  —  perhaps  one  in  five.    During 
the  first  half  of  the  last  century  there  were  nine  of  this  rank, 


424  MANUAL  OF  ASTRONOMY 

and  in  the  last  half  four,  five  of  which  were  notable.  The  most 
brilliant  of  these  appeared  in  1882. 

Since  then  there  have  been  several  that  could  be  seen  without 
a  telescope,  the  most  interesting  among  them  being  H alley's 
periodic  comet,  which  returned  to  perihelion  in  April,  1910.  In 
August,  1881,  for  a  few  days  two  conspicuous  comets  —  one 
magnificent  one,  and  the  other  more  than  respectable  —  shone 
together  in  the  northern  heavens  not  very  far  apart,  a  thing 
almost,  if  not  quite,  unprecedented. 

The  total  number  that  visit  the  solar  system  must  be  enor- 
mous, since,  although  even  with  the  telescope  we  can  see  only 
the  comparatively  few  which  come  near  the  earth  and  are  favor- 
ably situated  for  observation,  yet  not  infrequently  from  five  to 
eight  are  discovered  in  a  single  year  (ten  in  1898) ;  and  there 
is  seldom  a  day  when  one  is  not  present  somewhere  in  the  sky  : 
often  there  are  several. 

478.  Designation  of  Comets A  remarkable  comet  gener- 
ally bears  the  name  of  its  discoverer  or  of  some  one  who  has 
acquired  its  "  ownership,"  so  to  speak,  by  some  important 
research  respecting  it.  Thus,  we  have  Halley's,  Encke's,  and 
Donati's  comets.  The  common  herd  are  distinguished  only 
by  the  year  of  discovery,  with  a  letter  indicating  the  order  of 
discovery  in  that  year,  as  comet  #,  6,  c,  1895 ;  or,  still  again,  by 
the  year,  with  a  Roman  numeral  denoting  the  order  of  perihelion 
passage.  Thus,  Donati's  comet,  which  is  "comet/,  1858,"  is 
also  "  comet  1858-VI,"  and  this  is  the  more  scientific  designa- 
tion, and  is  generally  used  in  catalogues  of  comets. 

Comet  a  is  not,  however,  always  comet  I,  for  comet  b  may 
outrun  it  in  reaching  the  perihelion,  and  it  often  happens  that 
a  comet's  perihelion  passage  does  not  occur  in  the  same  year 
as  its  discovery. 

In  some  cases  a  comet  bears  a  double  name,  as,  for  instance, 
the  Pons-Brooks  comet,  which  was  first  discovered  by  Pons  in 
1812,  and  on  its  return  in  1883,  by  Brooks. 


COMETS  425 

479.  Discovery  of  Comets.  —  Asa  rule,  these  bodies  are  first  Their 
found  by  comet  hunters,  who  make  a  business  of  searching  for  dlscoverv' 
them.     For  this  purpose  they  usually  employ  a  telescope  known 

as  a  "  comet-seeker,"  carrying  an  eyepiece  of  low  power,  with  a 
large  field  of  view.  When  first  seen  a  comet  is  usually  a  mere 
roundish  patch  of  faintly  luminous  cloud,  which,  if  really  a 
comet,  will  reveal  its  true  character  within  an  hour  or  two  by 
its  motion. 

Some  observers  have  found  a  great  number  of  these  bodies.  Messier 
discovered  thirteen  between  1760  and  1798,  and  Pons  twenty-seven  between 
1800  and  1827.  In  this  country  Brooks,  Barnard,  and  Swift  have  been 
especially  successful.  It  occasionally  happens,  however,  as  with  Holmes' 
comet  of  1892,  and  Rordame's  comet  of  1893,  that  a  comet  is  picked  up 
with  the  naked  eye  by  some  one  not  an  astronomer  at  all. 

Recently  several  have  been  discovered  by  photography,  the  first  by  Bar- 
nard at  the  Lick  Observatory  in  1892,  another  by  Chase  in  1898  while 
trying  to  photograph  November  meteors.  Halley's  comet  was  photographed 
in  1909  before  it  could  be  observed  visually. 

480.  Duration  of  Visibility,  and  Brightness.  —  The  comet  of  Duration  o 
1811  was  observed  for  seventeen  months;  the  great  comet  of  vlslbllltv- 
1861  for  a  year;  and  comet  1889-1  was  followed  at  the  Lick 
Observatory  for  nearly  two  years,  —  the  longest  period  of  visi- 
bility yet  recorded.     On  the  other  hand,  the  comet  is  some- 
times visible  only  a  week  or  two,  and  twice  a  comet  near  the 

sun  has  been  photographed  during  a  total  eclipse,  —  never  seen 
before  or  after  the  two  minutes  of  totality.  The  average  dura- 
tion of  visibility  is  probably  not  far  from  three  months. 

As  to  brightness,  comets  differ  widely.     About  one  in  four  or  Their 
five  reaches  the  naked-eye  limit  at  some  point  in  its  orbit,  and  a  brightpess 
very  few,  say  two  or  three  in  a  century,  are  bright  enough  to  be 
seen  in  the  daytime.     The  comets  of  1843  and  1882  were  the 
last  so  observed. 


426 


MANUAL  OF   ASTRONOMY 


Ancient 
ideas  as 
to  their 
motion. 


Tycho  estab- 
lishes their 
astro- 
nomical 
character. 


Suggestion 
of  parabolic 
orbits  by 
Hevelius. 


Relative 
numbers  of 
parabolic, 
elliptical, 
and  hyper- 
bolic orbits. 


THEIR   ORBITS 

481.  The  ideas  of  the  ancients  as  to  the  motions  of  these 
bodies  were  very  vague.     Aristotle  and  his  school  considered 
them  to  be  merely  exhalations  from  the  earth,  inflamed  in  the 
upper  air,  and  therefore  meteorological  bodies,  and  not  astro- 
nomical at  all.     Seneca,  indeed,  held  a  more  correct  opinion, 
but  it  was  shared  by  few ;  and  Ptolemy  fails  to  recognize  them 
as  heavenly  bodies  in  his  Almagest. 

Tycho  was  the  first  to  establish  their  rank  as  truly  "celes- 
tial," by  comparing  the  observations  of  the  comet  of  1577,  made 
in  different  parts  of  Europe,  and  showing  that  its  parallax  was 
less,  and  its  distance  greater,  than  that  of  the  moon. 

Kepler  supposed  that  they  moved  in  straight  lines  and  seems 
to  have  been  more  than  half  disposed  to  consider  them  as  living 
beings,  traveling  through  space  with  will  and  purpose,  "like 
fishes  in  the  sea." 

Hevelius  in  1675  was  the  first  to  suggest  that  their  orbits 
might  be  parabolas,  and  his  pupil  Doerfel  proved  this  to  be  the 
case  in  1681  for  the  comet  of  that  year.  The  theory  of  gravi- 
tation had  now  appeared,  and  Newton  soon  worked  out  and 
published  a  method  by  which  the  elements  of  a  comet's  orbit 
can  be  determined  from  the  observations. 

482,  Relative  Numbers  of  Parabolic,  Elliptical,  and  Hyperbolic 
Orbits. — A  large  majority  move  in  orbits  that  are  sensibly  parab- 
olas.    Out  of  nearly  four  hundred  orbits  computed  up  to  1901, 
more  than  three  hundred  are  of  this  kind.     About  eighty-five 
are  more  or  less   distinctly  elliptical,  and  about  half  a  dozen 
seem  to  be  hyperbolas,  but  hyperbolas  differing  so  slightly  from 
the  parabola  that  the  hyperbolic  character  is  not  certain  in  a 
single  one  of  the  cases. 

Comets  which  have  elliptical  orbits  of  course  return,  if 
undisturbed,  at  regular  intervals ;  the  others  visit  the  sun 
only  once,  and  never  come  back. 


COMETS 


427 


The  difficulty  of  determining  whether  a  particular  comet  is  Difficulty  of 

or  is  not  periodic  is  much  increased  by  the  fact  that  comets  rec°gmzmg 

J  a  comet 

have  no  characteristic  "  personal  appearance,"  so  to  speak,  by  when  it 

which  a  given  individual  can  be  recognized  whenever  seen,  —  returns, 
as  Jupiter  or  Saturn  could  be,  for  instance.     It  is  necessary  to 
depend  almost  entirely  upon  the  elements  of  its  orbit  for  the 


FIG.  159,  — The  Close  Coincidence  of  Different  Species  of  Cometary  Orbits 
within  the  Earth's  Orbit 

recognition  of  a  returning  comet,  and  this  is  not  always  satis- 
factory, since  there  are  a  number  of  cases  in  which  several 
distinct  comets  move  in  orbits  almost  identical.  (See  Sec.  487.) 

483.   Elements  of  a  Comet's  Orbit.  —  As   in   the   case   of  a  Elements  of. 
planet,  three  perfect  observations  of  a  comet's  place  are  thec-  acomet's 


retically  sufficient  to  determine  its  entire  orbit. 


orbit  deter- 
Practically,    mined  by 

however,  it  is  not  possible  to  observe  a  comet  with  anything  three  com- 

....._.  pleteobser- 

like  the  accuracy  of  a  planet  (on  account  of  its  indefinite  out-  yations. 
line),  nor  usually  with  sufficient  exactness  to  determine  positively 


428 


MANUAL    OF   ASTRONOMY 


Uncertainty 
as  to  major 
axis  and 
period. 


Parabolic 
orbit  has 
but  five 
elements. 


from  a  small  number  of  observations  whether  the  orbit  is  or 
is  not  parabolic. 

The  plane  of  the  orbit  and  its  perihelion  distance  can,  in  most 
cases,  be  fairly  settled  without  any  difficulty;  but  the  eccen- 
tricity and  the  major  axis,  with  its  corresponding  period,  require 
a  long  series  of  observations  for  their  determination  and  are 
seldom  ascertained  with  much  precision  from  a  single  appear- 
ance of  the  comet.  In  that  part  of  the  comet's  path  which  can 
be  observed  from  the  earth  the  three  kinds  of  orbits  usually 
diverge  but  little ;  indeed,  they  may  almost  coincide  (as  shown 
in  Fig.  159). 

For  a  parabolic  orbit  the  elements  to  be  computed  are  only 
five  in  number,  instead  of  seven,  as  in  the  case  of  an  ellipse. 
The  semi-major  axis  and  period  (which  are  infinite)  drop  out, 
as  does  the  eccentricity,  which  is  necessarily  unity.  To  define 
the  size  of  the  orbit  the  perihelion  distance,  p,  takes  the  place 
of  the  semi-major  axis. 

For  the  parabolic  elements  we  have,  therefore,  (1)  p,  peri- 
helion distance,  (2)  i,  inclination  of  the  orbit  to  the  ecliptic, 
(3)  &,  the  longitude  of  the  ascending  node,  (4)  o>,  angle 
between  line  of  nodes  and  perihelion,  (5)  T,  date  of  perihelion 
passage. 

It  must  be  distinctly  understood,  moreover,  that  orbits  which  are 
"sensibly"  parabolic  are  seldom,  if  ever,  strictly  so, — the  chances  are 
infinity  to  one  against  an  exact  parabola.  If  a  comet  were  moving  at  any 
time  in  such  a  curve,  the  slightest  retardation  due  to  the  disturbing  force 
of  any  planet  would  change  this  parabola  into  an  ellipse,  and  the  slightest 
acceleration  would  make  an  hyperbola  of  it. 

Effect  of  It  should  be  noted  also  that  if  a  comet's  orbit  is  nearly  para- 

shght  change  j^]^  a  verv  slight  change  in  the  velocity  of  the  comet's  motion 
velocity  upon  will  cause  an  enormous  change  in  the  computed  major  axis  and 
major  axis  period.  This  is  obvious  from  the  equation  (Sec.  320) 

and  period  in  * 

cases  of  r  / 

orbitsnearly  =2\Ty 

parabolic.  "*  ^ 


COMETS 


429 


When  V  nearly  equals  U  (as  must  be  the  case  if  the  orbit  is 
nearly  a  parabola)  the  denominator  will  be  extremely  small, 
and  a  very  trifling  change  in  V  will  make  a  great  percentage  of 
change  in  the  difference  between  U2  and  F2,  and  will  affect  a, 
the  semi-major  axis,  accordingly. 

484.  The  Elliptic  Comets.  —  The  first  comet  ascertained  to 
move  in  an  elliptical  orbit  was  that  known  as  Halley's,  which 
has  a  period  of  about  seventy-six  years,  its  periodicity  having 
been  announced  by  Hal- 
ley  in  1705.  It  has  since 
been  observed  in  1759 
and  1835  and  again  in 
1909  and  1910. 

The  second  of  the 
periodic  comets  in  order 
of  discovery  is  Encke's, 
with  the  shortest  period 
known,  less  than  three 
and  one-half  years.  Its 
periodicity  was  discov- 
ered in  1819. 

About  a  dozen  of  the 
comets  to  which  compu- 
tation assigns  elliptic 
orbits  have  periods  so 

long --near  or  exceeding  one  thousand  years — that  their  real 
character  is  still  rather  doubtful.  About  seventy-five,  however, 
have  orbits  which  are  distinctly  and  certainly  elliptical,  and 
about  sixty  of  them  have  periods  of  less  than  one  hundred 
years.  About  twenty  have  been  actually  observed  at  two  or 
more  returns  to  perihelion;  as  to  the  rest  of  the  sixty,  several 
are  now  expected  within  a  few  years,  and  many  have  prob- 
ably been  lost  to  observation,  either  from  disintegration,  like 
Biela's  comet  (soon  to  be  discussed),  or  by  having  their  orbits 


Elliptic 
orbits. 


Halley's 
comet. 


Encke'p 
comet. 


FIG.  160.  — Orbits  of  Short-Period  Comets 


About 

twenty 

comets  of 

which 

return  has 

been 

observed. 


430 


MANUAL   OF   ASTRONOMY 


The  comet- 
families  of 
Jupiter, 
Saturn, 
Uranus,  and 
Neptune. 


The  capture 
theory. 


transformed  by  perturbations,  so   that   they  no   longer   come 
within  the  range  of  observation. 

Fig.  160  shows  the  orbits  of  five  of  the  short-period  comets 
(as  many  as  can  be  shown  without  confusion)  and  also  a  part 
of  the  orbit  of  Halley's  comet.  These  five  particular  comets, 
and  about  twenty-five  more,  all  have  periods  ranging  from  three 
and  one-half  to  eight  years,  and  they  all  pass  very  near  the 
orbit  of  Jupiter.  Moreover,  each  comet's  orbit  crosses  that  of 
Jupiter  near  one  of  its  nodes,  marked  by  a  short  cross  line  on 
the  comet's  orbit.  The  fact  is  extremely  significant,  showing 
that  these  comets  at  times  come  very  near  to  Jupiter,  and  it 
points  to  an  almost  certain  connection  between  that  planet  and 
these  bodies. 

485.  Comet-Families ;  Origin  of  Periodic  Comets. — It  is  clear, 
as  has  been  said,  that  the  comets  which  move  in  parabolic  orbits 
cannot  well  have  originated  within  the  limits  of  the  solar  system, 
but  must  have  come  from  a  great  distance.     As  to  those  which 
move  in  elliptical  orbits,  it  is  a  question  whether  we  are  to 
regard  them  as  native  to  the  system  or  only  as  "naturalized," 
or  perhaps  mere  sojourners  for  a  time ;  but  it  is  evident  that  in 
some  way  many  of  them  stand  in  peculiar  relations  to  Jupiter 
and  to  other  planets. 

The  short-period  comets,  those  which  have  periods  ranging 
from  three  to  eight  years,  are  now  recognized  and  spoken  of  as 
Jupiter's  family  of  comets.  About  thirty  are  known  already,  of 
which  fifteen  have  been  observed  twice  or  oftener,  —  some  of 
them  a  dozen  times.  Similarly,  Saturn  is  credited  with  two 
comets;  Uranus  with  two,  one  of  which  is  Ternpel's  comet, 
closely  connected  with  the  November  meteors  and  due  to  appear 
in  1900,  but  not  seen.  Finally,  Neptune  has  a  family  of  six ; 
among  them  Halley's  comet,  and  two  others  which  have  returned 
a  second  time  to  perihelion  since  1880. 

486.  The  Capture  Theory. — The  now  generally  accepted  expla- 
nation as  to  the  origin  of  these  comet-families  was  first  suggested 


COMETS  431 

by  Laplace;  viz.,  that  the  comets  which  compose  them  have  been 
"captured"  by  the  planet  to  which  they  stand  related. 

A  comet  entering  the  system  in  a  parabolic  orbit  and  pass- 
ing near  the  planet  will  be  disturbed  and  either  accelerated  or 
retarded.  If  it  is  accelerated,  then  according  to  equation  (4) 
(Sec.  320),  the  major  axis  will  become  negative,  the  orbit  will  Effect  of 
be  changed  to  an  hyperbola,  and  the  comet  will  never  be  seen 
again.  But  if  the  comet  is  retarded,  the  semi-major  axis  will  tionto 

become  finite  and  the  orbit  will  be  made  elliptical,  so  that  the  transforma 

parabolic 
comet  will  return  at  each  revolution  to  the  place  where  it  was  orbit. 

first  disturbed ;  it  will  become  a  periodic  comet,  with  its  orbit 
passing  near  to  the  orbit  of  the  disturbing  planet. 

It  will  not,  however,  as  students  sometimes  imagine,  revolve 
around  its  capturer  like  a  satellite.  The  focus  of  its  new  and 
diminished  orbit  still  remains  at  the  sun. 

But  this  is  not  all.     After  a  certain  time  the  planet  and  the  Subsequent 
comet  will  be  sure  to  come  together  again  at  or  near  this  place.   ^^ 
The  result  then  may  be  an  acceleration  which  will  enlarge  the  and  planet, 
comet's  orbit,  or  even  transform  it  to  a  parabola  or  hyperbola ; 
but  it  is  an  even  chance  at  least  that  the  result  may  be  a  retarda- 
tion and  that  the  orbit  and  period  may  thus  be  further  dimin- 
ished.   This  may  happen  over  and  over  again,  until  the  comet's 
orbit  falls  so  far  inside  that  of  the  planet  that  it  suffers  no 
further  disturbance  to  speak  of. 

Given  time  enough  and  comets  enough,  the  ultimate  result 
would  necessarily  be  such  a  comet  family  as  really  exists.  It 
is  not  permanent,  however;  sooner  or  later,  if  a  captured  comet 
is  not  first  disintegrated,  it  will  almost  certainly  encounter  its 
planet  under  such  conditions  as  to  be  thrown  out  of  the  system. 

A  recent  investigation,  however,  by  Callandreau,  upon  the  Caiian- 
disintegration  of   comets  by  the   action  of   the   sun  and  the  f^e^tiga- 
planet  Jupiter,  shows  that  the  limit  of  distance  at  which  such  tion  on  the 
an  effect  is  possible  is  quite  considerable,  and  that  the  breaking  peaking  up 
up  of  a  comet  ought  not  to  be  very  unusual.     He  suggests  that 


432 


MANUAL   OF   ASTRONOMY 


the  number  of  the  comets  of  Jupiter's  family  has  probably  thus 
been  largely  increased  by  the  division  of  single  comets  into 
several,  —  a  suggestion  which  greatly  relieves  very  serious 
objections  that  have  been  urged  against  the  capture  theory. 

487,  Comet-Groups.  —  There  are  several  instances  in  which  a 
number  of  comets,  certainly  distinct,  chase  each  other  along 
almost  exactly  the  same  path,  at  an  interval  usually  of  a  few 
months  or  years,  though  they  sometimes  appear  simultaneously. 
The  most  remarkable  of  these  comet-groups  is  that  composed 
of  the  great  comets  of  1668,  1843,  1882,  and  1887.     These 
have  all  come  in  from  the  direction  (nearly)  of  Sirius  and  have 
receded  nearly  on  that  line,  passing  close  around  the  sun  and 
actually  through  the  corona.    As  Professor  Comstock  has  pointed 
out,  they  are  all  of  them,  if  their  computed  orbits  can  be  trusted, 
now  (1902)  bunched  together  in  a  space  hardly  bigger  than  the 
sun,  at  a  distance  of  about  150  radii  of  our  orbit,  and  are  moving 
away  together  very  slowly. 

It  is,  of  course,  nearly  certain  that  the  comets  of  such  a  group 
have  a  common  origin,  perhaps  from  the  disruption  of  a  single 
comet  by  the  attraction  of  the  sun  or  a  planet,  in  accordance 
with  the  suggestion  of  Callandreau  just  mentioned. 

The  distinction  between  comet-families  and  comet-groups 
must  be  carefully  noted :  in  the  former  the  orbits  agree  only  in 
passing  close  to  that  of  the  capturing  planet;  in  the  latter  the 
orbits  are  nearly  identical,  at  least  in  the  part  near  the  sun. 

488.  Perihelion  Distance,  etc.  —  The   perihelion   distances   of 
comets    differ   greatly.      Eight   of   the    300    computed    orbits 
approach  the  sun  within  less  than  6  000000   miles,  and  four 
have  a  perihelion  distance  exceeding  200  000000.      A  single 
comet,  that  of  1729,  had  a  perihelion  distance  of  more  than 
four  astronomical  units,  or  375  000000  miles;  this  is  one  of  the 
half  dozen  possibly  hyperbolic  comets,  and  must  have  been  an 
enormous  one  to  be  visible   at  such  a  distance.     There  may, 
of  course,  be  any  number  of  comets  with  still  greater  perihelion 


COMETS  433 

distances,  because,  as  a  rule,  we  are  able  to  see  only  such  as 
come  reasonably  near  to  the  earth's  orbit,  —  probably  but  a 
small  percentage  of  the  total  number  that  visit  the  sun.  It 
has  been  computed  that  something  like  six  thousand  come 
within  the  orbit  of  Jupiter  every  year. 

The  inclinations  of  cometary  orbits  range  all  the  way  from  inclination 
zero  to  90°,  but  most  of  the  short-period  comets  have  orbits  ^^^ 
of  small  inclination,  as  might  be  expected,  since  such  comets 
would  be  much  more  likely  to  suffer  capture  than  those  that 
cross  the  planes  of  the  planetary  orbits  at  a  high  angle. 

As  regards  the  direction  of  motion,  the  six  hyperbolic  comets  Direction  of 
and  all  the  elliptical  comets  having  periods  of  less  than  one  motlon- 
hundred  years  move  direct,  excepting  only  Halley's  comet  and 
Tempel's  comet  of  1866.     The  rest  show  no  decided  preponder- 
ance either  way. 

489,   Comets  are  Visitors.  —  The  fact  that  the  orbits  of  most  Comets  are 
comets  are  sensibly  parabolic,  and  that  their  planes  have  no  evi-  visitors  to 

J  L  the  solar 

dent  relation  to  the  ecliptic,  apparently  indicates  (though  it  does  system. 
not  absolutely  demonstrate)  that  these  bodies  do  not  in  any 
proper  sense  belong  to  the  solar  system.  They  come  to  us  with 
just  the  velocity  they  would  have  if  falling  towards  the  sun 
from  an  enormous  distance,  and  they  leave  the  system  with  a 
velocity  which,  if  no  force  but  the  sun's  attraction  acts  upon 
them,  will  carry  them  away  to  an  infinite  distance,  or  until  they 
encounter  the  attraction  of  some  other  sun. 

Their  motions  are  just  what  might  be  expected  of  ponderable 
masses  moving  in  empty  space  between  the  stars  under  the  law 
of  gravitation. 

There  are  difficulties  with  the  theory  that  the  comets  come  to  Difficulty 
us  from  space  among  the  stars,  chiefly  depending  upon  the  now  ™*£  ky- 
certain  fact  that  the  solar  system  is  traveling  at  the  rate  of  they  come 


several  miles  a  second  (Sec.  543)  and  that,  therefore,  comets  from  stellar 

11  i  regions. 

composed  of  matter  met  by  us  ought  to  have  a  relative  velocity, 
with    respect   to   the    sun,  so   great  as   to  produce   numerous 


434 


MANUAL   OF   ASTRONOMY 


The  home 
of  the 
comets. 


Peculiar 
behavior  of 
Encke's 
comet. 


Paradoxical 
increase  of 
speed  as 
result  of 
resistance. 


hyperbolic  orbits,  whereas  we  find  few  such,  if  any.  Then,  too, 
there  ought  to  be  a  marked  concentration  of  the  axes  of  cometary 
orbits  near  the  direction  towards  which  the  sun  is  moving. 

While  the  investigations  of  the  late  Professor  Newton  of 
New  Haven  partially  relieve  the  difficulty,  astronomers  still 
feel  it;  and  many  are  disposed  to  think  that  our  solar  system, 
in  its  journey  through  space,  is  accompanied  by  far-distant, 
outlying  clouds  of  nebulous  matter,  which  are  the  source  and 
original  "home  of  the  comets,"  to  borrow  Professor  Peirce's 
expression. 

490.  Acceleration  of  Encke's  Comet.  —  With  one  remarkable 
exception,  the  motions  of  comets  appear  to  be  just  what  would 
be  expected  of  masses  moving  in  free  space  under  the  law  of 
gravitation.  The  single  exception  is  in  the  case  of  Encke's 
comet,  which,  since  its  first  discovery  in  the  last  century  (its 
periodicity  was  not  discovered  until  1819),  has  been  continu- 
ally quickening  its  speed  and  shortening  its  period.  In  1819 
its  period  was  1205  days.  Between  1820  and  1860  each  suc- 
cessive period  shortened  about  two  and  one-half  hours;  from 
1860  to  1870  the  shortening  was  only  one  and  three-fourths 
hours  to  each  revolution,  and  since  then  it  has  increased  to 
about  two  hours.  The  period  at  present  is  about  fifty-four 
hours  shorter  than  in  1819,  and  the  mean  distance  from  the 
sun  is  nearly  a  quarter  of  a  million  of  miles  less  than  then. 

No  perturbations  by  any  known  body  will  account  for  such 
an  acceleration,  and  thus  far  no  reasonable  explanation  has  been 
suggested  as  even  possible,  except  that  something  encountered 
in  its  motion  through  interstellar  space  retards  the  comet,  just 
as  air  retards  a  rifle  bullet. 

At  first  sight  it  seems  almost  paradoxical  that  a  resistance 
should  accelerate  a  comet's  speed,  but  referring  to  Sec.  320  we 
see  that  any  diminution  of  the  velocity  will  also  diminish  the 
semi-major  axis.  This  will  reduce  the  period,  which  is  propor- 
tional to  Vo^,  by  a  greater  percentage  than  it  will  reduce  the 


COMETS  485 

circumference  of  the  orbit,  which  is  simply  proportional  to  a ;  as 
a  consequence  there  will  be  an  increase  of  velocity  above  what 
the  comet  had  in  the  larger  orbit.  A  corned  gains  more  speed 
ly  falling  nearer  to  the  sun  than  it  loses  by  the  direct  effect  of 
the  resistance.  If  this  action  continues  without  cessation,  the 
ultimate  result  must  be  a  spiral  whiding  inward  until  the  comet 
strikes  the  surface  of  the  sun. 

When  this  peculiar  behavior  was  first  discovered  by  Encke  it  was 
ascribed  to  the  action  of  a  resisting  medium  and  adduced  as  proof  of 
the  existence  of  the  "  luminiferous  ether."  But  since  no  other  comets 
exhibit  the  same  effect,  and  the  effect  upon  Encke's  comet  itself  varies  in 
amount  from  time  to  time,  it  is  now.  generally  attributed  to  something 
encountered  along  the  orbit  of  this  particular  body ;  possibly  the  passage 
through  some  cloud  of  meteors,  or  disturbances  by  some  unknown  body  in 
the  asteroidal  regions. 

THE   COMETS   THEMSELVES 

491.   Physical  Characteristics  of  Comets.  —  The  orbits  of  these  Physical 
bodies  are  now  thoroughly  understood,  and  their  motions  are  °haractert 
calculable  with  as  much  accuracy  as  the  nature  of  the  observa- 
tions permit;  but  we  find  in  their  physical  constitution  and 
behavior  some  of  the  most  perplexing  and  baffling  problems  in 
the   whole  range  of  astronomy,  —  apparent   paradoxes  which 
have  not  yet  received  a  satisfactory  explanation. 

While  comets  are  evidently  subject  to  the  attraction  of  gravi- 
tation, as  shown  by  their  orbits,  they  also  exhibit  evidence  of 
being  acted  upon  by  powerful  repulsive  forces  emanating  from 
the  sun.     While  they  shine  partly  by  reflected  light,  they  are 
also  certainly  self-luminous,  their  light  being  generated  in  a  way  Non- 
not  yet  thoroughly  explained.     They  are  the  bulkiest  bodies  Planetary 
known,  except  the  nebulae,  in  some  cases  thousands  of  times  ities. 
larger  than  the  sun  or  stars ;  but  in  mass  they  are  "  airy  noth- 
ings,"  and  one  of   the  smaller  asteroids  probably  rivals  the 
largest  of  them  in  weight. 


436 


MANUAL    OF   ASTRONOMY 


The  coma. 


The  nucleus. 


The  train, 
tail,  or 
beard. 


Jets  and 
envelopes. 


Dimensions 
of  heads  of 
comets. 


492,  The  Constituent  Parts  of  a  Comet.  —  (a)  The    essential 
part  of  a  comet  —  that  which  is  always  present  and  gives  the 
comet  its  name  —  is  the  coma,  or  nebulosity,  a  hazy  cloud  of 
faintly  luminous  transparent  matter. 

(b)  Next,  we  have  the  nucleus,  which,  however,  makes  its 
appearance  only  when  the  comet  is  near  the  sun,  and  is  wanting 
in  many  comets.     It  is  a  bright,  more  or  less  starlike  point 
near  the  center  of  the  coma,  and  is  usually  the  object  "  observed 
on  "  in  noting  a  comet's  place.     In  some  cases  the  nucleus  is 
double,  or  even  multiple. 

(c)  The  tail,  or  train,  is  a  stream  of  light  which  commonly 
accompanies  a  bright  comet  and  is  sometimes  present  even  with 
a  telescopic  one.     As  the  comet  approaches  the  sun  the  tail 
follows  it,  but  as  the  comet  moves  away  from  the  sun  it  pre- 
cedes, and  by  the  ancients  was  then  called  the  beard.     Speaking 
broadly,  the  train  is  always  directed  away  from  the  sun,  though 
its  precise  form  and  position  are  determined  partly  by  the  comet's 
motion.     It  is  practically  certain  that  it  consists  of  extremely 
rarefied  matter,  which  is  thrown  off  by  the  comet  and  powerfully 
repelled  by  the  sun.     It  certainly  is  not  —  like  the  smoke  of  a 
locomotive  or  the  train  of  a  meteor — matter  simply  left  behind. 

(d)  Jets  and  Envelopes.     The  head  of  a  brilliant  comet  is 
often  veined  by  jets  of  light,  which  appear  to  be  spirted  out 
from  the  nucleus  ;  and  sometimes  it  throws  off  a  series  of  concen- 
tric envelopes  like  hollow  shells,  one  within  the  other.     These 
phenomena,  however,  are  seldom  observed  in  any  but  brilliant 
comets. 

493.  Dimensions  of  Comets.  —  The   volume,   or   bulk,    of   a 
comet  is  often  enormous,  —  almost  beyond  conception  if  the 
tail  is  included  in  the  estimate.     The  head,  or  coma,  is  usually 
from  40000  to  150000  miles  in  diameter;   a  comet  less  than 
10000  miles  in  diameter  would  stand  little  chance  of  discovery, 
and  comets  exceeding  150000  miles  are  rather  unusual,  though 
there  are  a  considerable  number  on  record. 


COMETS  437 

The  head  of  the  comet  of  1811  at  one  time  measured  nearly  1  200000 
miles,  —  more  than  forty  per  cent  larger  than  the  diameter  of  the  sun  itself . 
Holmes'  comet  of  1892  had  at  one  time  a  diameter  exceeding  700000  miles, 
but  no  visible  nucleus  at  that  time.  A  few  weeks  later  it  looked  like  a 
mere  hazy  star.  The  comet  of  1680  had  a  head  600000  miles  across,  and 
that  of  Donati's  comet  of  1858  was  250000  miles  in  diameter. 

The  diameter  of  the  head  changes  all  the  time,  and  what  is 
singular  is,  that  while  the  comet  is  approaching  the  sun,  the 
head  ordinarily  contracts,  expanding  again  as  it  recedes.     The  Contraction 
diameter  of  Encke's  comet  shrinks  from  about  300000  miles  ofhead 

when  near 

when  it  is  130  000000  miles  from  the  sun  to  a  diameter  not  the  sun. 
exceeding  12000  or  14000  miles  when  at  perihelion,  a  distance 
of  33  000000  miles,  the  variation  in  bulk  being  more  than 
10000  to  1.  No  satisfactory  explanation  is  known,  but  Sir 
John  Herschel  has  suggested  that  the  change  may  be  merely 
optical,  —  that  near  the  sun  a  part  of  the  nebulous  matter  is 
evaporated  by  the  solar  heat  and  so  becomes  invisible,  con- 
densing and  reappearing  again  when  the  comet  reaches  cooler 
regions. 

The  nucleus  usually  has  a  diameter  ranging  from  a  mere  point  Diameter  of 
less  than  100  miles  in  diameter  up  to  5000  or  6000,  or  even  the  nucleus- 
more.     Like  the  comet's  head,  it  also  changes  in  diameter,  even 
from  day  to   day.     The  variations,  however,  do  not  seem  to 
depend  in  any  regular  way  upon  the  comet's  distance  from 
the  sun,  but  rather  upon  its  activity  in  throwing  off  jets  and 
envelopes. 

The  tail  of  a  comet,  as  regards  simple  magnitude,  is  by  far  its  Dimensions 
most  imposing  feature.     Its  length  is  seldom  less  than  5  000000  of  the  tram' 
or  10  000000  miles ;  it  frequently  attains  50  000000,  and  there 
are  several  cases  in  which  it  has  exceeded  100  000000.     It  is 
usually  more  or  less  fan-shaped,  so  that  at  the  outer  extremity 
it  is  millions  of  miles  across,  being  shaped  roughly  like  a  cone 
projecting  behind  the  comet  from  the  sun,  and  more  or  less  bent  its  usual 
like  a  horn,  as  shown  in  Fig.  158.     The  volume  of  the  train  of  form' 


438 


MANUAL   OF   ASTRONOMY 


Mass  of 
comets 
extremely 
small. 


Nature  of 
the  evi- 
dence. 


May  equal 
mass  of  an 
iron  ball 
150  miles  in 
diameter. 


the  comet  of  1882,  110  000000  miles  in  length,  some  200000 
miles  in  diameter  at  the  comet's  head,  and  with  a  diameter 
of  10  000000  or  12  000000  at  its  extremity,  exceeded  the  bulk 
of  the  sun  itself  more  than  eight  thousand  times. 

494.  Mass  of  Comets.  —  While  the  volume  of  comets  is  thus 
enormous,  their  mass  is  apparently  insignificant,  —  in  no  case 
at  all  comparable  even  with  that  of  our  little  earth. 

The  evidence  on  this  point,  however,  is  purely  negative ;  it 
does  not  enable  us  in  any  case  to  determine  how  great  the  mass 
really  is,  but  only  how  great  it  is  not ;  i.e.,  it  only  proves  that 
the  comet's  mass  is  less  than  a  certain  very  small  fraction  of  the 
earth's,  but  does  not  warrant  us  in  setting  any  lower  limit. 

The  evidence  is  derived  from  the  fact  that  no  sensible  pertur- 
bations have  ever  been  produced  in  the  motions  of  the  planets 
or  their  satellites  even  when  comets  have  come  very  near  them ; 
and  yet  in  such  a  case  the  comet  itself  is  "  sent  kiting  "  in  a 
new  orbit,  showing  that  gravitation  is  fully  operative  between 
the  comet  and  the  planet. 

Lexell's  comet  in  1770,  and  Biela's  comet  on  several  occa- 
sions, came  so  near  the  earth  that  the  length  of  the  comet's 
period  was  greatly  changed,  while  the  year  was  not  altered  by 
so  much  as  a  single  second ;  and  it  would  have  been  changed 
by  many  seconds  if  the  comet's  mass  were  as  much  as  -J-Q-^HJ  °^ 
that  of  the  earth. 

Brooks'  comet  of  1886  actually  passed  between  Jupiter  and 
the  orbit  of  its  first  satellite.  None  of  the  satellites  were 
sensibly  disturbed,  but  the  comet's  orbit  was  changed  from  an 
ellipse  with  a  period  of  over  thirty  years  to  one  of  a  period 
with  less  than  seven. 

At  present  this  mass  (^  WTOT  °^  ^e  ear^n's  mass)  is  very  gen- 
erally assumed  as  a  probable  upper  limit  for  even  a  large  comet. 
It  is  about  ten  times  the  mass  of  the  earth's  atmosphere  and  is 
about  equal  to  the  mass  of  a  ball  of  iron  150  miles  in  diameter, 
but  how  much  smaller  the  limit  may  really  be  no  one  can  say. 


COMETS  439 

495.    Density  of  Comets.  —  The  mean  density  is  necessarily  Mean 

extremely  low,  the  mass  of  the  comet  being  so  small  and  the  density°f 

J  comets  very 

volume  so  great.     If   the    head    of  a  comet   50000   miles  in  low.    Com- 

diameter  has  the  very  improbable  mass  of  TTrnVnTT  of  that  of  the  Parablewith 

,  an  air-pump 

earth,  its  mean  density  is  only  about  Q-^-Q-Q  part  or  that  of  the 


vacuum. 


air  at  the  earth's  surface,  —  a  degree  of  rarefaction  reached  by 
only  the  very  best  air-pumps. 

The  extremely  low  density  of  comets  is  shown  also  by  their 
transparency.     Small  stars  are  often  seen  directly  through  the  Transpar- 
head  of  a  comet  100000  miles  in  diameter,  even  very  near  its  ency°f 

^  cometa 

nucleus,  and  with  hardly  a  perceptible  diminution  of  luster. 
There  are,  however,  in  such  cases  indications  of  a  very  slight 
refraction  of  the  light  passing  through  the  comet,  causing  a 
barely  sensible  displacement  of  the  star. 

As  for  the  tail,  the  density  of  this  must  be  almost  infinitely  Still  lower 
lower  than  that  of  the  head,  —  far  below  the  best  vacuum  we  can  density  of 

the  tram. 

make  by  any  means  of  science.  It  is  nearer  to  an  airy  nothing 
than  anything  else  we  know  of. 

Another  point  should  be  referred  to.     Students  often  find  it 
hard  to  conceive  how  such  impalpable  "dust  clouds"  can  move  Dust  clouds 
in  orbits  like  solid  masses  and  with  such  enormous  velocities  ;  traverse 

interplan- 

they  forget  that  in  a  vacuum  a  feather  falls  as  swiftly  as  a  stone.  etary  space 
Interplanetary  space  is  a  vacuum,  far  more  perfect  than  any-  as  swiftly 
thing  we  can  produce  by  artificial  means,  and  in  it  the  lightest  bo(jies. 
bodies  move  as  freely  and  swiftly  as  the  densest,  since  there  is 
nothing  to  resist  their  motion.     If  all  the  earth  were  suddenly 
annihilated,  except  a  single  feather,  the  feather  would   keep 
on  and  pursue  the  same  orbit,  with  the  unchanged  speed  of 
18  \  miles  a  second. 

496.    Nature  of  Comets.  —  We  must  bear  in  mind,  however,  LOW  mean 
that  the  low  mean  density  of  the  comet  does  not  necessarily  j^^pa™ 
imply  that  the   density  of  its  constituent  parts  is   small.     A  biewith 
comet  may  be  in  the  main  composed  of  small  heavy  bodies  and  oJ 
still  have  a  very  low  mean  density,  provided  they  are  widely  ent  parts. 


440 


MANUAL   OF   ASTRONOMY 


Comets 
probably 
swarms  of 
small  solid 


The  light  of 
comets  not 
reflected 
sunlight 
though 
largely  due 
to  action  of 
solar  rays. 


Capricious 
variations. 


The  ordi- 
nary comet 
spectrum. 


enough  separated.  There  is  much  reason,  as  we  shall  see,  for 
supposing  that  such  is  really  the  case,  —  that  the  comet  is 
largely  composed  of  small  meteoric  sand  grains  (say  pinheads, 
many  feet  apart),  each  carrying  with  it  a  certain  quantity  of 
enveloping  gas,  in  which  light  is  produced  either  by  electric 
discharges  or  by  some  different  action  due  to  the  rays  of 
the  sun. 

As  to  the  size  of  the  particles  opinions  vary  widely:  some 
maintain  that  they  are  large  rocks  ;  Professor  Newton.  calls  a 
comet  a  "  gravel  bank  "  ;  others  think  it  a  mere  "  dust  cloud  " 
or  "  smoke  wreath." 

The  unquestionable  and  close  connection  between  comets  and 
meteors,  which  we  shall  soon  discuss,  almost  compels  some 
"meteoric  hypothesis,"  and,  at  present  at  least,  no  other  theory 
is  maintained  by  any  high  authorities. 

497.  The  Light  of  Comets.  —  To  some  extent  this  is  reflected 
sunshine,  but  in  the  main  it  is  light  emitted  by  the  comet  itself 
under  the  stimulus  of  solar  action.  That  the  light  depends  in 
some  way  upon  the  sun  is  shown  by  the  fact  that  its  intensity 
follows  approximately  the  same  law  as  the  brightness  of  a 

planet,  and  is  usually  proportional  to  -  —  -,  in  which  R  is  the 


comet's  distance  from  the  sun  and  A  its  distance  from  the  earth. 

A  comet  as  it  recedes  from  the  earth  does  not  simply  grow 
smaller,  retaining  the  same  apparent  intrinsic  brightness,  as 
would  be  the  case  with  an  independently  self-luminous  body, 
but  grows  fainter  and  disappears  on  account  of  faintness. 

Not  infrequently,  however,  the  light  of  a  comet  varies  capri- 
ciously, brightening  and  fading  without  apparent  cause,  within 
a  few  days  or  even  a  few  hours. 

498.  Spectra  of  Comets.  —  The  spectrum  is  usually  a  faint 
continuous  spectrum,  on  which  are  superposed  certain  bright 
bands,  five  of  them  in  the  visible  spectrum  ;  there  are  others 
in  the  ultra-violet,  observable  only  by  photography.  Of  the 


COMETS 


441 


five  visible  bands,  two  are  very  faint,  so  that  ordinarily  but 
three  can  be  seen.  The  spectrum  is  identical  with  that  of  the 
blue  cone  at  the  base  of  a  Bunsen-burner  flame,  which  is  always 
found  where  hydrocarbon  gases  are  in  a  state  of  combustion, 
and  is  generally  ascribed  to  acetylene.  (See  Fig.  161,  comet, 
1881-III.)  Other  bright  bands  have  also  been  photographed 


FIG.  161.  — Comet  Spectra 

For  convenience  in  engraving,  the  dark  lines  of  the  solar  spectrum  in  the  lowest 
strip  of  the  figure  are  represented  as  bright 

in  the  ultra-violet,  some  of  them  evidently  due  to  cyanogen, 
a  compound  of  carbon  and  nitrogen,  and  others  not  certainly 
identified. 

The  faint  continuous  spectrum  is  due,  in  part  at  least,  to 
reflected  sunlight,  as  shown  by  the  fact  that  some  of  the  prin- 
cipal Fraunhofer  lines  have  been  photographed  in  it,  though 
they  cannot  be  seen. 

If  the  nucleus  is  bright,  its  spectrum  also  appears  like  a 
narrow  streak,  nearly  continuous,  running  through  the  spec- 
trum of  the  head,  as  shown  in  the  figure.  At  least  ninety  per 


442 


MANUAL   OF   ASTRONOMY 


cent  of  all  the  comets  thus  far  observed  have  given  this  hydro- 
carbon (acetylene?)  spectrum. 

If  the  comet  is  one  that  does  not  approach  the  sun  within  the 
distance  of  100  000000  miles  or  so  (such  comets  are  not  numer- 
ous), the  hydrocarbon  bands  are  sometimes  missing,  replaced  in 
some  cases  by  unidentified  bands  of  a  different  wave-length,  as 
in  the  case  of  Brorsen's  comet  and  Borrelly's  comet  of  1877 
(Fig.  161). 

The  spectrum  of  Holmes'  comet  of  1892,  which  never  came 
inside  the  earth's  orbit,  showed  no  bands  or  lines  at  all,  either 
bright  or  dark,  but  was  simply  continuous. 

If,  on  the  other  hand,  the  comet  approaches  the  sun  within 
8  000000  or  10  000000  miles,  the  hydrocarbon  bands  grow 
relatively  faint,  and  the  yellow  line  of  sodium  becomes  domi- 
nant, as  in  Wells'  comet,  1882-1,  and  the  great  comet, 
1882-11. 

The  latter,  indeed,  which  almost  grazed  the  surface  of  the 
sun,  showed  numerous  bright  lines  of  other  substances  (prob- 
ably iron  for  one). 

It  has  been  maintained  by  Sir  Norman  Lockyer  that  the 
comet's  spectrum  changes  regularly  and  progressively  with  dis- 
tance from  the  sun,  the  bands  not  only  altering  their  appear- 
ance, but  slightly  shifting  their  position ;  but  the  evidence  for 
this  is  not  conclusive. 

As  to  the  cause  of  luminosity,  it  is  practically  agreed  that  it 
cannot  be  due  to  any  general  heating  of  the  mass  of  the  comet, 
of  which  the  mean  temperature,  on  the  contrary,  is  probably 
extremely  low.  The  explanation  now  most  favored  attributes 
the  light  to  electric  discharges  between  the  solid  (?)  particles 
through  the  gases  which  envelop  them,  —  discharges  due  to 
inductive  action  of  the  sun  on  the  "  cometic "  cloud  rushing 
towards  it  from  regions  of  space,  where  the  electric  potential  is 
presumably  different  from  that  of  the  sun  itself.  At  present 
we  can  assign  no  certain  reason  for  such  difference,  but,  on  the 


COMETS  443 

other  hand,  there  is  not  any  known  reason  for  assuming  a 
uniform  electric  potential  through  all  space.     (See  Sec.  502.) 

It  is,  perhaps,  necessary  to  remark  that  while  the  hydrocarbon  Comet  not 
bands  of  the  spectrum  demonstrate  the  presence  of  hydrocarbons  r  amly  corn" 
in  the  comet,  they  do  not  at  all  prove  that  the  comet  is  mainly  hydro- 
composed  of  them,  nor  even  that  they  constitute  a  considerable  carbons- 
portion  of  its  mass.    It  is  much  more  likely  that  the  minute  solid 
or  liquid  particles  constitute  ninety  per  cent  of  the  whole. 


FIG.  162.  —  Head  of  Donati's  Comet 
Bond 

499,   Phenomena  that  accompany  the  Comet's  Approach  to  the  Phenomena 
Sun.  —  When  a  comet  is  first  discovered  it  is  usually,  as  has  resultmg 
been  already  said,  a  mere  round  nebulosity,  a  little  brighter  pr0achto 
near  the  middle.     As  it  approaches  the  sun  it  brightens  rapidly,  tne  sun- 
and   the   nucleus   appears.     Then   on   the   sunward   side   the 
nucleus  appears  to  emit  luminous  jets,  or  to  throw  off  more  or 
less  symmetrical  envelopes,  which  follow  each  other  at  intervals 
of  a  few  hours,  expanding  and  growing  fainter,  until  they  are 
lost  in  the  general  nebulosity  of  the  head. 


444 


MANUAL  OF   ASTRONOMY 


To  Sun 


Fig.  162  shows  the  envelopes  as  they  appear  in  the  head 
of  Donati's  comet  of  1858.  At  one  time  seven  of  them 
were  visible  at  once ;  very  few  comets,  however,  exhibit 
the  phenomena  with  such  symmetry.  More  frequently  the 
emissions  from  the  nucleus  take  the  form  of  mere  jets  and 
streamers. 

500.  Formation  of  the  Tail —  The  tail  appears  to  be  formed 
of  material  first  projected  from  the  nucleus  towards  the  sun  and 
afterwards  repelled  both  by  nucleus  and  sun,  as  illustrated  by 

Fig.  163.  At  least,  this  theory 
has  the  great  advantage  over 
all  others  which  have  been  pro- 
posed (there  have  been  many  of 
them)  that  it  not  only  accounts 
for  the  phenomenon  in  a  general 
way,  but  admits  of  being  worked 
out  in  detail  and  verified  mathe- 
matically, by  comparing  the 
actual  size  and  form  of  the  comet's 
tail  at  different  points  in  the  orbit 
with  that  indicated  by  theory; 
Comet's  an(j  the  accordance  is  usually 
satisfactory. 

According  to  this  theory,  the 

tail  is  simply  an  assemblage  of  repelled  particles,  each  moving 
in  its  own  hyperbolic  orbit1  around  the  sun,  the  separate 
particles  having  very  little  connection  with,  or  effect  upon,  each 

1  Since  the  assumed  repulsive  force  upon  a  particle  virtually  diminishes  the 
sun's  attraction  upon  it,  it  also  virtually  diminishes  its  parabolic  velocity  (i.e., 
if  under  this  diminished  attraction  the  particle  had  fallen  from  an  infinite 
distance,  its  parabolic  velocity  would  be  less  than  if  gravitation  had  acted 
unmodified).  In  the  formula  of  Sec.  320,  U2,  if  the  comet  is  moving  in  a 
parabola,  therefore  becomes  less  than  V2  for  the  particles  that  compose  the 
tail ;  and  the  semi-major  axis,  a,  for  the  subsequent  orbit  of  such  particles, 
becomes  negative,  converting  their  orbits  into  hyperbolas. 


FIG.  163.  —  Formation    of 
Tail  by  Matter  expelled  from   the 
Head 


COMETS  445 

other  and  being  almost  entirely  emancipated  from  the  control 
of  the  comet's  head. 

Since  the  force  of  the  projection  from  the  comet  is  seldom 
very  great,  all  these  orbits  lie  nearly  in  the  plane  of  the  comet's 
orbit,  and  the  result  is  that  the  tail  is  usually  a  sort  of  a  flat,  The  tail 
hollow,  curved,  horn-shaped  cone,  open  at  the  large  end.     The  usually  a 
edges  of  the  tail,  near  the  comet  at  least,  therefore   usually  curved  cone, 
appear  much  brighter  than  the  central  part. 

501.   Curvature  of  the  Tail,  and  Tails  of  Different  Types. - 
The  tail  is  curved,  because  the  repelled  particles,  after  leaving  Explanation 

of  curva- 
ture. 


FIG.  164.  —  A  Comet's  Tail  at  Different  Points  in  its  Orbit 
near  Perihelion 

the  comet's  head  and  receding  from  the  sun,  retain  their  origi- 
nal motion,  and  in  consequence  are  arranged,  not  along  a 
straight  line  drawn  from  the  sun  to  the  comet,  but  on  a  curve 
convex  to  the  direction  of  the  comet's  motion,  as  shown  in 
Fig.  164,  —  the  stronger  the  repulsion,  the  less  the  curvature. 

Bredichin  of  Moscow  has  found  that  in  this  respect  the  trains  The  three 
of  comets  may  be  classified  under  three  different  types  :  types  °f 

First,  the  long,  straight  rays:  they  are  composed  of  matter  tails, 
upon  which  the  solar  repulsion  is  from  twelve  to  fifteen  times  as 


446 


MANUAL   OF   ASTRONOMY 


The 

hydrogenous 

tail. 


The  hydro- 
carbon tail. 


Tails  due 
to  metallic 
vapors. 


Nature  of 
the  repulsive 
force:  the 
electrical 
theory. 


great  as  gravitational  attraction,  so  that  the  particles  leave 
the  comet  with  a  relative  velocity  of  4  or  5  miles  a  second, 
which  is  afterwards  continually  increased  until  it  becomes 
enormous.  The  nearly  straight  rays,  shown  in  Fig.  158,  tan- 
gent to  the  principal  tail  of  Donati's  comet,  belong  to  this 
class.  For  plausible  reasons,  connected  with  the  low  density 
of  hydrogen,  Bredichin  considers  them  to  be  composed  of  that 
substance,  possibly  set  free  by  the  decomposition  of  hydrocar- 
bons. They  are  rather  uncommon,  and  in  no  case  since  the 
promulgation  of  the  theory  have  been  bright  enough  to  allow  a 
spectroscopic  test  of  their  nature. 

The  second  type  is  the  curved,  plumelike  train,  like  the  prin- 
cipal train  of  Donati's  comet.  In  trains  of  this  type,  supposed 
to  be  due  to  hydrocarbon  vapors,  the  repulsive  force  varies  from 
2.2  times  the  gravitational  attraction  for  particles  on  the  convex 
edge  of  the  train  to  half  that  amount  for  those  on  the  inner 
edge.  Trains  of  this  class  show  the  hydrocarbon  spectrum 
through  all  their  extent. 

Third.  A  few  comets  show  tails  of  still  a  third  type,  —  short, 
stubby  brushes,  violently  curved,  and  due  to  matter  upon  which 
the  repulsive  force  is  feeble  as  compared  with  gravity.  These 
are  assigned  to  metallic  vapors  of  considerable  density,  sodium 
perhaps,  possibly  sometimes  iron. 

502.  The  Repulsive  Force.  —  The  nature  of  the  force  which 
repels  the  particles  of  a  comet  is,  of  course,  only  a  matter  of 
speculation.  There  is  probably  at  present  a  decided  preponder- 
ance of  opinion  in  favor  of  the  idea  that  it  is  electrical.  In  this 
case  the  repulsion  upon  small  particles,  being  a  surface  action, 
would  be  more  effective  in  proportion  as  the  particle  was  smaller, 
and  this  is  in  accordance  with  the  apparent  fact  that  the  molecules 
of  hydrogen,  hydrocarbon  gas,  and  metallic  vapors  are  sorted 
out,  so  to  speak,  to  form  the  three  different  types  of  tails. 

But  the  experiments  of  Nichols  and  Hull  in  this  country  and 
of  Lebedew  in  Russia,  made  independently  in  1901,  tend  to 


COMETS  447 

confirm  a  long-standing  surmise   that  it  may  be  due    to  the  Repulsion 
direct  action  of  the  waves  of  solar  radiation  upon  extremely  due  to  d!rect 

J    action  of 

small  particles  of  matter.  light-waves. 

Maxwell,  years  ago,  showed  that  as  a  consequence  of  his  electromagnetic 
theory  of  light  (then  new,  but  now  almost  universally  accepted),  a  particle 
receiving  light-rays  ought  to  be  repelled  by  a  force  the  amount  of  which 
he  computed.  For  particles  of  sensible  magnitude  the  calculated  force 
is  insignificant  as  compared  with  the  solar  attraction,  but  for  particles 
—  say,  a  hundred  thousandth  of  an  inch  in  diameter  —  it  many  times 
exceeds  that  attraction.  Various  unsuccessful  attempts  have  been  made 
to  detect  such  a  force  experimentally,  but  at  last  the  physicists  seem  to 
have  overcome  the  difficulties,  and  their  result  practically  agrees  with 
Maxwell's  prediction.  This  theory  is  supplementary  to  the  electrical 
rather  than  contradictory,  as  the  repulsive  force  of  light  is  due  to  an 
electromagnetic  reaction,  and  it  is  not  unlikely  that  the  particles  repelled 
may  carry  electric  charges. 

It  has  also  been  attempted  to  account  for  the  repulsion  by  an  indirect   Evaporation 
action  resulting  from  the  heating  of  the  surfaces  of  the  almost  innnitesi-  theory, 
mal  particles  on  the  side  next  to  the  sun. 

There  is  no  reason  to  suppose  that  the  matter  driven  off  to  form 
the  tail  is  ever  recovered  ly  the  comet.  It  probably  remains  in 
space,  to  be  picked  up  by  any  large  masses  which  the  particles 
may  meet. 

Whenever  a  comet  comes  near  to  the  sun  or  to  one  of  the 
larger  planets,  it  is  subjected  to  forces  which  tend  to  pull  it 
to  pieces,  and,  as  the  mutual  attraction  between  its  particles 
is  extremely  feeble,  it  sometimes  happens  that  it  is  separated 
into  several  portions,  as  was  the  case  with  Biela's  comet  in 
1846,  with  the  great  comet  of  1882,  and  with  Brooks'  comet 
of  1889.  Indeed,  it  seems  likely  that  all  along  its  course  it  Disintegra- 
loses  portions  of  its  substance,  so  that  at  each  successive  return  tlon  of 

*  comets. 

to  perihelion  it  becomes  smaller  and  finally  ceases  to  exist 
as  a  recognizable  "body,"  the  scattered  particles  traveling  by 
themselves  until  they  fall  upon  some  larger  body  as  "shooting- 
stars." 


448 


MANUAL   OF   ASTRONOMY 


Unexplained  503.  Unexplained  and  Anomalous  Phenomena.  —  A  curious 
phenomena.  phenomenoll)  not  yet  explained,  is  the  dark  stripe  which  in 
the  case  of  a  large  comet  nearing  the  sun  runs  down  the 
center  of  the  tail,  looking  very  much  as  if  it  were  a  shadow 
of  the  comet's  head.  It  is  certainly  not  a  shadow,  however, 
because  it  usually  makes  more  or  less  of  an  angle  with  the 
sun's  direction.  It  is  well  shown  in  Fig.  162.  When  the 
comet  is  at  a  greater  distance  from  the  sun  this  central  stripe 
is  usually  bright,  as  in  Fig.  165.  Indeed  many,  perhaps  most, 
small  comets,  instead  of  the  usual  hollow,  horn-shaped  tail, 
show  only  this  narrow  streak,  smaller  in  diameter  than  the 
comet's  head,  —  as  if  the  material  repelled  by  the  sun  fol- 
lowed around  the  coma  and  left  it 
only  at  the  point  remotest  from  the 
sun. 

Not  infrequently,  however,  comets 
possess  anomalous  tails,  —  usually 
in  addition  to  the  normal  tail,  but 

of 

directed  sometimes  straight  towards 
the  sun  and  sometimes  nearly  at  right  angles  to  that  direction. 

The  great  comet  of  1882  also  carried  with  it  for  a  time  a 
faintly  luminous  "  sheath,"  which  seemed  to  envelop  the  comet 
itself  and  that  portion  of  the  tail  near  the  head,  projecting  2° 
or  3°  forward  towards  the  sun.  For  some  days,  moreover,  it 
was  accompanied  by  little  clouds  of  cometary  matter,  which 
left  the  main  comet,  like  smoke  puffs  from  a  bursting  bomb, 
and  traveled  off  at  an  angle  until  they  faded  away.  None  of 
these  appearances  contradict  the  theory  outlined  above,  but  they 
cannot  be  said  to  be  explained  by  it,  —  evidently  we  have  not 
yet  the  whole  story. 

504.  Photography  of  Comecs. — It  is  not  unlikely  that  photog- 
raphy will  give  us  light  on  the  subject,  for  the  sensitive  plate 
reveals  in  the  tail  of  the  comet  (not  in  the  head)  many  interesting 


Peculiar 
features  of 
the  great 
comet  of 
1882. 


Photog- 
raphy of 
comets. 


COMETS 


449 


details  which  are  wholly  invisible  to  the  eye ;  partly,  it  is  likely, 
because  of  the  cumulative  action  of  the  feeble  light  during  a  long 
photographic  exposure,  and  partly,  also,  because  the  light  of  a 
comet's  tail  probably  resembles  that  of  the  positive  "  brush  "  from 
a  charged  electrode  in  being  very  rich  in  ultra-violet  rays,  which 
act  powerfully  in  photography,  but  do  not  affect  the  eye. 

The  first  photograph  of  a  comet  was  obtained  by  Bond  in 
1858,  —  only  a  partial  success  and  but  little  known.  .The  next 
was  in  1881*,  when  Henry  Draper  in  New  York  and  Huggins 
in  England  photographed  Tebbutt's  comet,  and  in  1882  the 
great  comet  was  well  photographed  by  Gill  in  South  Africa. 
Fig.  166  is  a  series 
of  photographs  of 
Swift's  comet  of 
1892  by  Barnard. 
The  tail  was  barely 
visible  to  the 
naked  eye,  and  the 
peculiar  features 
exhibited  in  the 
photograph  were 
not  visible  at  all. 

Fig.  167  is  from 
Hussey's  beautiful 

photograph  of  Rordame's  comet  of  1893,  for  which  we  are 
indebted  to  the  kindness  of  Professor  Holden. 

Since  in  photographing  a  comet  the  camera  is  kept  pointed  at 
the  head,  which  is  moving  more  or  less  rapidly  among  the  stars, 
the  star  images,  during  the  long  exposure,  are  drawn  out  into 
parallel  streaks,  as  seen  in  the  photograph.  The  little  irregu- 
larities are  due  to  faults  of  the  driving  clock  and  vibrations  of 
the  telescope  and  atmosphere. 

The  knots  and  streamers,  which  in  the  photographs  charac- 
terize the  comet's  tail,  were  none  of  them  visible  in  the  telescope 


FIG.  166.  —  Swift's  Comet  of  1892 


Rordame's 
comet  of 
1893. 


450 


-MANUAL   OF   ASTRONOMY 


FIG.  167.  —  Rordame's  Comet,  July  13, 1893 
Prom  photograph  by  W.  J.  Hussey,  at  the  Lick  Observatory 


COMETS 


451 


and  differ  from  those  shown  upon  plates  preceding  and  follow- 
ing. Other  plates  of  Rordame's  comet,  made  on  the  same 
evening  a  few  hours  earlier  and  later,  indicate  that  these  knots 
were  swiftly  receding  from  the  comet's  head  at  a  rate  exceeding 
150000  miles  an  hour. 

Fig.  168  is  a  photograph  (also  by  Barnard)  of  Gale's  comet 
(May,  1894).  It  was  moving  through  a  crowd  of  stars. 

In  several  cases,  as  already  mentioned,  comets  have  been 
discovered  by  photography. 

505.  Danger  from  Comets.  — 
We  close  the  chapter  with  a  few 
remarks  upon  a  subject  which 
has  been  much  discussed. 

It  has  been  supposed  that 
comets  might  do  us  harm  in 
two  ways,  —  either  by  actually 
striking  the  earth  or  by  falling 
into  the  sun,  and  thus  pro- 
ducing such  an  increase  of 
solar  heat  as  to  burn  us  up. 

As  regards  collision  with  a 
comet,  there  is  no  question  that 
the  event  is  possible.  In  fact, 
if  the  earth  lasts  long  enough,  it  is  practically  sure  to  happen , 
for  there  are  several  comets  whose  orbits  pass  nearer  to'  our 
own  than  the  semidiameter  of  the  comet's  head,  and  at  some 
time  the  earth  and  comet,  if  the  comet  lasts  long  enough,  will 
certainly  come  together. 

As  to  the  consequence  of  such  a  collision  it  is  impossible  to 
speak  positively,  for  want  of  sure  knowledge  of  the  constitution 
of  the  comet.  If  the  theory  which  has  been  presented  is  true, 
everything  depends  on  the  size  of  the  separate  particles  which 
form  the  main  portion  of  the  comet's  mass.  If  they  weigh 
tons,  the  bombardment  experienced  by  the  earth  when  struck 


Rapid 
motion  of 
knots  in  tail 
of  comet. 


comet. 


Possibility 
of  collision 
with  comet. 


xNx\VC^  ^X 


fc*v 


FIG.  168.  —  Gale's  Comet,  May  5, 1894 


Probability 
that  col- 
lision would 
be  harmless 
to  the  earth 


452  MANUAL   OF   ASTRONOMY 

by  a  comet  would  be  a  very  serious  matter ;  if,  as  seems  much 
more  likely,  they  are  for  the  most  part  smaller  than  pinheads, 
the  result  would  be  simply  a  splendid  shower  of  shooting-stars. 
In  1861  the  earth  actually  passed  unnoticed  through  the  tail  of 
the  great  comet  of  that  year. 

Such  encounters  will,  however,  be  very  rare;  if  we  accept 
the  estimate  of  Babinet,  they  ought  to  occur  once  in  about 
15  000000  years  in  the  long  run. 

A  danger  of  a  different  sort  has  been  suggested,  —  that 
if  a  comet  were  to  strike  the  earth,  our  atmosphere  would 
be  poisoned  by  the  mixture  with  the  gaseous  components  of 
the  comet.  Here,  again,  the  probability  is  that  on  account 
of  the  low  density  of  the  cometary  matter  no  sufficient  amount 
would  remain  in  the  air  to  do  any  mischief  at  the  earth's 
surface. 

Possible  fall  506.  Effect  of  the  Fall  of  a  Comet  into  the  Sun.  —  As  to  this, 
int^thlfsun  ^  may  ^e  s^a^e(^  that,  except  in  the  case  of  Encke's  comet,  there 
is  no  evidence  of  any  action  going  on  that  would  cause  a  now 
existing  periodic  comet  to  strike  the  sun's  surface;  it  is,  how- 
ever, doubtless  possible,  perhaps  not  improbable,  that  a  comet 
may  sometime  enter  the  system  from  without,  so  accurately 
aimed  as  to  hit  the  sun. 

But  in  that  case  it  is  not  likely  that  the  least  mischief  would 

be  done.     If  a  comet  with  a  mass  equal  to  y-Q-oVn'o  °^  *ne  eapth's 

mass  were  to  strike  the  sun's  surface  with  the  parabolic  velocity 

Probably  no  of  nearly  400  miles  a  second,  the  energy  of  impact  converted 

harm  except  'n^o  neaj.  wou}(j  generate  about  as  many  calories  of  heat  as  the 

to  the  comet.  J 

sun  radiates  in  eight  or  nine  hours.  If  this  were  all  instantly 
effective  in  producing  increased  radiation  at  the  sun's  surface 
(increasing  it,  say,  eightfold,  for  even  a  single  hour),  harm 
would  doubtless  follow;  but  it  is  practically  certain  that 
nothing  of  the  sort  would  happen.  The  cometary  particles 
would  pierce  the  photosphere  and  liberate  their  heat  mostly 
below  the  solar  surface,  simply  expanding,  by  some  slight 


COMETS  453 

amount,  the  sun's  diameter,  and  so  adding  to  its  store  of 
potential  energy  about  as  much  as  it  ordinarily  expends  in  a 
few  hours  and  postponing,  by  so  much,  the  date  of  its  final 
solidification.  There  might,  and  very  likely  would,  be  a  flash 
of  some  kind  at  the  solar  surface  as  the  shower  of  cometary 
particles  struck  it,  but  probably  nothing  that  the  astronomer 
would  not  take  delight  in  watching. 

EXERCISES 

1.  What  would  be  the  mean  density,  compared  with  air,  of  the  spherical 
head  of  a  comet  100000  miles  in  diameter  and  having  a  mass  T(Tinnn>  that 
of  the  earth,  assuming  the  density  of  the  earth  to  be  5.53  times  that  of 
water  and  the  density  of  water  773  times  that  of  air?     Ans.    About  ^oo- 

2.  What  would  be  the  diameter  of  such  a  comet  if  compressed  to  a 
density  the  same  as  that  of  the  earth?  Ans.    171  miles. 

3.  Can  the  dimensions   of  a  comet's  tail  be  determined  with  much 
accuracy  ?     If  not,  why  not  ? 

4.  How  can  it  happen  that  comets  whose  orbits  nearly  coincide  within 
a  distance  of  100  000000  miles  from  the  sun  may  have  periods  differing  by 
hundreds  of  years?     For  example,  the  comets  of  1880  and  1882,  of  which 
the  first  has  a  computed  period  of  only  33  years,  and  the  other  of  more 
than  600. 

5.  In  the  case  of  two  cometary  orbits  very  nearly  parabolic,  and  having 
the  same  very  small  perihelion  distance,  how  would  the  ratio  of  their  major 
axes  be  affected  by  a  small  diff erence  in  their  perihelion  velocities  ?     (See 
Sec.  320,  remembering  that,  as  the  orbits  are  nearly  parabolic,  V2  must  be 
very  nearly  equal  to  U2  when  the  comets  pass  perihelion.) 

6.  If  the  repulsive  force  of  the  sun  upon  a  particle  of  a  comet's  tail 
were  just  equal  to  the  gravitational  attraction  (Sec.  502),  what  would  be 
the  path  of  that  particle?  Ans.    A  straight  line. 

7.  If  the  repulsive  force  exceeded  the  gravitational  attraction,  what 
would  be  the  nature  of  the  path? 

Ans.  An  orbit  convex  toward  the  sun,  hyperbolic  if  the  repulsion 
varied  inversely  as  the  square  of  the  distance,  the  sun  being  in  the 
focus  outside  the  curve,  i.e.,  at  F"  in  Fig.  119,  Sec.  314. 


454 


MANUAL   OF   ASTRONOMY 


8.  What  would  be  the  path  if  the  repulsive  force  were  only  very  small 
as  compared  with  the  gravitational  attraction  ? 

Ans.   An  orbit  of  slightly  greater  major  axis  and  period  than  that 
of  the  comet  itself. 

9.  Will  a  given  comet  (say  Encke's)  have  precisely  the  same  orbit  on 
successive  returns  ? 

10.  Why  can  we  not  infer  with  certainty  that  two  comets  which  have 
orbits  practically  identical  are  themselves  identical  ? 

11.  Can  we,  from  spectroscopic  observations  of  a  comet,  infer  the  rela- 
tive proportions  of  the  luminous  and  non-luminous  substances  present  in 
the  comet? 

12.  Is  it  probable  that  a  comet  can  continue  permanently  in  the  solar 
system  as  a  comet  ?     If  not,  why  not,  and  what  will  become  of  it  ? 


Potsdam  Astrophysical  Observatory 


CHAPTER   XVII 
METEORS   AND    SHOOTING-STARS 

Aerolites :  their  Fall  and  Physical  Characteristics ;  Cause  of  Light  and  Heat ;  Prob- 
able Origin  —  Shooting-Stars :  their  Number,  Velocity,  and  Length  of  Path  — 
Meteoric  Showers :  the  Radiant ;  Connection  between  Comets  and  Meteors 

METEORS 

507.  Meteorites,  or  Ae'rolites.  —  Occasionally  bodies  fall  upon 
the  earth  out  of  the  sky,  coming  to  us  from  outer  space.  Until  they 
reach  our  air  they  are  invisible,  but  as  soon  as  they  enter  it  frhey 
blaze  out,  become  conspicuous,  and  the  pieces  which  fall  from 
them  are  called  meteorites,  aerolites,  or  simply  meteoric  stones. 

If  the  fall  occurs  at  night,  a  ball  of  fire  is  seen,  which  moves  Circum- 
with  an  apparent  velocity  depending  upon  the  distance  of  the  *^™* of 
meteor  and  the  direction  of  its  motion,  and  is  generally  followed  aerolites, 
by  a  luminous  train,  which  sometimes  remains  visible  for  many 
minutes  after  the  meteor  itself  has  disappeared.     The  motion 
is  usually  somewhat  irregular,  and  here  arid  there  along  its 
path  the  fire-ball  throws  off  sparks  and  fragments  and  changes 
its  course  more  or  less  abruptly.    Sometimes  it  vanishes  by  simply 
fading  out  in  the  distance,  sometimes  by  bursting  like  a  rocket. 

If  the  observer  is  near  enough,  the  flight  is  accompanied  by 
a  heavy  continuous  roar,  like  that  of  a  passing  railway  train, 
accentuated  now  and  then  by  violent  detonations ;  the  noise  is 
frequently  heard  50  miles  away,  especially  the  final  explosion.  Delay  of 
The  observer,  however,  must  not  expect  to  hear  the  explosion  sound  of 

explosipn 

when  he  sees  it.  Sound  travels  only  about  12  miles  a  minute, 
so  that  there  is  often  an  interval  of  several  minutes  between 
the  visible  bursting  and  its  report. 

455 


456 


MANUAL   OF  ASTRONOMY 


Size  of 
aerolites 


Aerolites 

mostly 

stones. 


Number  of 
meteorites 
collected 
since  1800. 


Iron 

meteorites 
of  which  the 
fall  was 
observed. 


If  the  fall  occurs  by  day,  the  luminous  appearances  are 
mainly  wanting,  though  sometimes  a  white  cloud  is  seen,  and 
even  the  train  may  be  visible.  In  a  few  cases,  aerolites  have 
fallen  almost  silently,  and  without  warning. 

508.  The  Aerolites  themselves.  —  The  mass  that  falls  is  some- 
times a  single  piece,  but  more  usually  there  are  many  fragments, 
sometimes  to  be  counted  by  thousands.  At  the  Pultusk  "  fall," 
in  1869,  the  number  was  estimated  to  exceed  100000,  mostly 
very  small.  The  pieces  weigh  from  500  pounds  to  a  few  grains, 
the  aggregate  mass  occasionally  amounting  to  more  than  a  ton. 
The  largest  single  mass,  so  far  as  known,  is  one  that  fell  at 
Knyahinya  in  1866,  weighing  647  pounds. 

By  far  the  greater  number  of  aerolites  are  stones,  but  a  few 
—  one  or  two  per  cent  of  the  whole  number  —  are  pieces  of 
nearly  pure  iron  more  or  less  alloyed  with  nickel. 

The  total  number  of  meteorites  which  have  fallen  and  been 
gathered  into  our  cabinets  since  1800  is  about  275.  The  only 
instances  in  which  purely  iron  meteorites  have  been  actually 
seen  to  fall  and  are  represented  by  specimens  in  our  cabinets 
are  the  eight  following,  viz.  : 

Agram,  Croatia,  Austria 1751 

Dickson  County,  Tennessee,  U.S 1835 

Braunau,  Bohemia 1847 

Victoria  West,  South  Africa 1862 

Nedagollah,  Arabia 1870 

Rowton,  England .  1876 

Mazapil,  Mexico 1885 

Cabin  Creek,  Arkansas,  U.S 1886 

There  are  about  as  many  more  which  contain  large  quantities 
of  iron  and  by  some  authorities  have  been  reckoned  as  "  irons"  ; 
nearly  all  meteorites  contain  a  large  percentage  of  the  metal, 
either  in  the  metallic  form  or  as  sulphid. 

About  30  of  the  275  fell  within  the  United  States,  the  most 
remarkable  being  those  of  Weston,  Conn.,  in  1807;  New 


METEORS   AND    SHOOTING-STARS  457 

Concord,  Ohio,  in  1860;  Amana,  Iowa,  1875;  Emmet  County, 
Iowa,  1879  (largely  iron) ;  and  Cabin  Creek,  Ark.,  1886. 

Our  cabinets  at  present  contain  specimens  of  somewhat  more  Total  num- 
than  three  hundred  meteors  which  have  been  seen  to  fall,  besides  be^.m 

cabinets. 

a  nearly  equal  number  of  other  bodies,  —  mostly  masses  of  iron 
which,  from  the  circumstances  of  their  finding  and  the  peculiari- 
ties of  their  constitution,  are  supposed  to  be  of  meteoric  origin. 

The  finest  collection  in  the  world  is  that  at  Vienna.  The  collection  of 
the  British  Museum  and  that  at  Paris  are  also  noteworthy ;  and  in  this 
country  the  cabinet  of  Yale  University  is  especially  rich. 

509,    Appearance  and  Constitution  of  the  Meteorites.  —  The  Appearance 
most  characteristic  external  feature  of  an  aerolite  is  the  thin  ffmej®or" 

lt<6S  I    TJIG 

black  crust  which  covers  it,  usually,  but  not  always,  glossy  crust, 
like  varnish.  It  is  formed  by  the  fusion  of  the  surface  in  the 
meteor's  swift  motion  through  the  air,  and  in  some  cases  pene- 
trates deeply  into  the  mass  through  veins  and  fissures.  It  is 
largely  composed  of  oxid  of  iron  and  is  almost  always  strongly 
magnetic.  The  crusted  surface  usually  exhibits  pits  and  hol- 
lows, called  "thumb-marks"  because  they  look  like  prints  pro- 
duced by  thrusting  the  thumb  into  a  piece  of  putty.  These 
cavities  are  explained  by  the  burning  out  of  certain  more  fusible 
substances  during  the  meteor's  flight. 

On  breaking,  the  stone  is  sometimes  found  to  be  compara-  internal 
tively  fine  grained,  but  usually  is  made  up  of  crystalline  lumps  structure- 
and  globules,  and  sometimes  has  a  considerable  portion  of  solid 
iron  scattered  throughout  the  mass  in  grains  as  large  as  a  pin- 
head  or  bird  shot. 

Twenty-seven  of  the  chemical  elements,  including  argon  and  Chemical 
helium,  have  been  found  in  meteorites,  but  not  a  single  new  elements: 
element.     Many   of  the  minerals  of  which  the  meteorites  are  minerals, 
composed  present  a  great  resemblance  to  terrestrial  minerals  of 
volcanic  origin,  but  there  are  also  many  which  are  peculiar  and 
not  found  on  the  earth. 


458 


MANUAL   OF   ASTRONOMY 


Path  and 
motion. 


Elevation 
when  first 
seen. 


Length  of 
path. 


The  occasional  presence  of  carbon  is  to  be  especially  noted ; 
and  in  a  meteor  which  fell  in  Russia  in  1887,  the  carbon 
appeared  to  be  in  a  crystalline  form,  identical  with  the  black 
diamond,  though  in  particles  exceedingly  minute. 

Fig.  169  is  from  a  photograph  of  a  fragment  of  one  of  the  meteoric 
stones  which  fell  at  Gross  Divina,  Hungary,  in  1837 ;  weight  about  twenty- 
four  pounds. 

510.  Path  and  Motion.  —  When  a  meteor  has  been  well 
observed  from  a  number  of  different  stations  a  considerable 


FIG.  169.  —  The  Gross  Divina  Meteorite 

distance  apart,  its  path  with  reference  to  the  surface  of  the 
earth  can  be  computed. 

It  is  found  that  it  usually  first  appears  at  an  altitude  of 
about  80  or  100  miles  and  disappears  at  a  height  of  from 
5  to  10.  The  length  of  the  path  is  generally  between  50 
and  500  miles,  though  in  some  cases  it  has  been  much  greater. 
In  1860  one  passed  from  over  Lake  Michigan  across  the 
country  and  fell  into  the  sea  beyond  Cape  May ;  and  in  1876 
a  great  meteor  traversed  the  country  from  Kansas  to  northern 
Pennsylvania. 


METEORS   AND   SHOOTING-STARS  459 

The  velocity  ranges  from  10  to  40  miles  a  second  in  the  Velocity, 
earlier  part  of  its  course,  but  is  very  rapidly  and  greatly 
reduced  by  the  resistance  of  the  atmosphere,  so  that  when  the 
surface  of  the  earth  is  reached  it  is  often  not  more  than  400  or 
500  feet  a  second.  In  one  case  (a  meteor  that  fell  near  Upsala, 
Sweden,  in  January,  1869)  several  of  the  stones  struck  upon 
the  ice  of  a  lake  and  rebounded  without  breaking  the  ice  or 
damaging  themselves. 

The  average  velocity  with  which  these  bodies  enter  the  air  Meteorites 
seems  to   be  very  near  the    parabolic  velocity  of    26   miles  a  arevisltors 

J  J  from  distant 

second,  due  to  the  sun  s  attraction  at  the  earth  s  distance,  —  just  regions. 
as  should  be  the  case,  if,  like  the  comets,  they  come  to  us  from 
distant  regions  of  space. 

511.  Observation  of  Meteors.  —  The   object  of  the  observer  observation 
should  be  to  obtain  as  accurate  an  estimate  as  possible  of  the  ofmeteors- 
altitude  and  azimuth  of  the  meteor  at  moments  which  can  be 
identified,  and  also  of  the  time  occupied  in  traversing  definite 
portions  of  the  path. 

By  night  the   stars  furnish  the  best  reference  points  from  Determi- 
which  to  determine  its  position.     By  day  one  must  take  advan-  nation  of 

,,.,,.  -i    n  i  meteor's 

tage  of  natural  objects  and  buildings   to   define   the  meteor  s  altitude  and 
place,  the  observer  marking  the  precise  spot  where  he  stood  azimuth, 
when  the  meteor  disappeared  behind  a  chimney,  for  instance,  or 
was  seen  to  burst  just  over  a  certain  branch  in  a  tree.     By  taking 
a  surveyor's  instrument  to  the  place  afterwards  it  is  then  easy 
to  translate  such  data  into  altitude  and  bearing. 

As  to  the  time  of  flight,  which  is  required  in  order  to  deter-  Time  of 
mine  the  meteor's  velocity,  it  is  usual  for  the  observer  to  begin 
to  repeat  rapidly  some  familiar  verse  of  doggerel  when  the 
meteor  is  first  seen,  reiterating  it  until  the  meteor  disappears. 
Then,  by  rehearsing  the  same  before  a  clock,  the  number  of 
seconds  can  be  pretty  accurately  determined. 

512.  Explanation  of  Heat  and  Light.  —  These  are  simply  due 
to  the  intense  condensation  of  the  air  before  the  swiftly  moving 


460 


MANUAL   OF   ASTRONOMY 


to  condensa- 
tion of  air 
in  front  of 
meteor. 


meteor,  and  consequent  destruction  of  the  meteor's  energy. 
Heating  due  The  resistance,  due  to  condensation,  amounts  in  many  cases  to 
the  back-pressure  of  hundreds  of  pounds  upon  a  square  inch ; 
and  most  of  the  energy  of  the  meteor  destroyed  in  this  way  is 
transformed  into  heat,  largely  imparted  to  the  air,  but  to  a 
considerable  extent  expended  upon  the  surface  of  the  meteor, 
fusing  it  and  producing  the  crust. 

If  a  moving  body  whose  mass  is  M  kilograms,  and  its  velocity 
V  kilometers  per  second,  is  stopped  by  a  resistance,  its  energy  is 
almost  entirely  converted  into  heat,  and  the  number  of  calories 
(Sec.  267)  developed  is  given  (approximately)  by  the  equation 


Formula  for 
amount  of 
heat  de- 
veloped. 


Virtual  tem- 
perature of 
air  en- 
countered 
is  that  of 
a  blowpipe 
flame. 


$  =  120  MV2. 

In  bringing  to  rest  a  body  having  a  mass  of  one  kilogram  and 
a  velocity  of  forty-two  kilometers,  or  26  miles  a  second,  the  quan- 
tity of  heat  developed  is  enormous, —  nearly  212000  calories, — 
vastly  more  than  sufficient  to  fuse  it,  even  if  it  were  made  of  the 
most  refractory  material.  As  Lord  Kelvin  has  shown,  the  ther- 
mal effect  of  the  rush  through  the  air  is  the  same  as  if  the  meteor 
were  immersed  in  a  blowpipe  flame  having  a  temperature  of 
many  thousand  degrees ;  and  it  is  to  be  noted  that  this  tempera- 
ture is  independent  of  the  density  of  the  air  through  which  the 
meteor  is  passing.  The  quantity  of  heat  developed  in  a  given 
time  is  greater,  of  course,  where  the  air  is  dense,  but  the  tempera- 
ture produced  in  the  air  itself  at  the  surface  where  it  encounters 
the  moving  body  is  the  same  whether  it  be  dense  or  rare. 

This  rise  of  temperature  is  due  to  the  fact  that  the  gaseous 
molecules  strike  the  surface  of  the  meteor  as  if  the  meteor  were 
at  rest  and  the  molecules  themselves  were  moving  with  speed 
correspondingly  increased.  (According  to  the  kinetic  theory 
of  gases,  the  "temperature"  of  a  gas  depends  entirely  upon 
the  mean  velocity  square  of  its  molecules.) 

When  the  moving  body  has  a  velocity  of  one  and  one-half 
kilometers  per  second  the  virtual  temperature  of  the  surrounding 


METEORS   AND    SHOOTING-STARS  461 

air  is   about    that  of   red   heat.     When  the   velocity  reaches 

thirty  kilometers  per  second  the  amount  of  heat  developed  is 

152,  or  225,  times  as  great,  and  the  surface  is  acted  upon  as  if 

the  surrounding  gas  were  a  blowpipe  flame,  as  has  been  said  ;  Formation 

the  surface  of  the  meteor  is  fused  and  the  liquefied  portion  is  ofcrust 

and  train. 

continually  swept  off  by  the  rush  of  air,  condensing  as  it  cools 
into  the  luminous  dust  that  forms  the  train.  The  fused  surface 
is  continually  renewed  until  the  velocity  falls  below  two  kilo- 
meters a  second,  or  thereabouts,  when  it  solidifies  and  forms 
the  crust. 

As  a  general  rule,  therefore,  the  fragments  are  hot  if  found  stones  some- 
soon  after  their  fall;  but  if  the  stone  is  a  large  one  and  falls  ^^f^nd 
nearly  vertically,  so  as  to  have  a  short  path  through  the  air,  the 
heating  effect  will  be  confined  to  its  surface,  and,  owing  to  the 
low  conducting  power  of  stone,  the   center  may  still  remain 
intensely  cold  for  some  time,  retaining  nearly  the  temperature 
which  it  had  in  interplanetary  space.     It  is  recorded  that  one 
of  the  fragments  of  the  Dhurmsala,  India,  meteorite,  which  fell 
in  1860,  was  found  in  moist  earth  half  an  hour  or  so  after  the 
fall  coated  with  ice. 

One    unexplained   feature   of   the  meteoric    trains    deserves  Unexplained 
notice.     They  often  remain  luminous  for  a  long  time,  some-  PhosPh°res- 

cence  of 

times  as  much  as  half  an  hour,  and  are  carried  by  the  wind  trains, 
like  clouds.  It  is  impossible  to  suppose  that  such  a  cloud  of 
impalpable  dust  remains  white-hot  for  so  long  a  time  in  the 
cold  upper  regions  of  the  atmosphere,  and  the  question  of  its 
enduring  luminosity  or  phosphorescence  is  an  interesting  and 
a  puzzling  one. 

513.  The  Origin  of  Meteors.  —  The  high  velocity  with  which 
many  enter  our  atmosphere  makes  it  quite  certain  that  they  at 
least  had  not  a  terrestrial  origin.  A  body  projected  from  the 
earth  could  never  return  with  higher  velocity  than  that  of  pro- 
jection, and  any  velocity  exceeding  about  7  miles  a  second  (the 
parabolic  velocity  at  the  earth's  surface  —  Sec,  319)  would  carry 


462 


MANUAL   OF   ASTRONOMY 


Meteors 
come  to  us 
as  astronom- 
ical bodies. 


Meteorites 
can  be 
classified. 


Theories  of 
their  origin. 


Iron  meteor- 
ites perhaps 
of  stellar 
origin. 


Professor 
Newton's 
results : 
some  meteor- 
ites perhaps 
asteroids. 


the  body  permanently  away  from  the  earth,  never  to  return 
unless  after  many  revolutions  around  the  sun.  Most  meteors, 
if  not  all,  come  to  us  as  astronomical  bodies,  moving  like  planets 
or  comets ;  as  to  their  origin,  we  can  only  speculate. 

At  the  same  time  we  find  in  our  cabinets  many  distinct 
classes  of  them,  and  in  each  class  all  the  meteors  which  com- 
pose it  resemble  each  other  so  closely  as  to  suggest  the  idea 
that  they  must  have  had  a  common  source,  or  at  one  time 
formed  portions  of  a  single  mass ;  but  where  and  when  ? 

Some  have  maintained  that  they  were  projected  from  lunar 
volcanoes,  ages  ago  perhaps  (for  lunar  volcanoes  are  now  inac- 
tive), and  that  since  that  time  they  have  been  moving  around 
the  sun  like  planets,  until  now  encountered  by  the  earth. 
Others  refer  them  to  similar  imagined  volcanic  eruptions  from 
the  earth  in  some  past  age,  and  others  consider  them  as  pro- 
ceeding from  the  disintegration  of  comets. 

As  to  the  iron  meteorites,  some  believe  that  they  have  been 
ejected  from  the  sun  or  from  a  star,  basing  the  opinion  upon  the 
remarkable  fact  that  these  meteoric  irons  are  usually  "soaked 
full "  of  occluded  gases,  —  hydrogen,  helium,  and  carbon  oxids, 
which  can  be  extracted  from  them  by  well-known  methods.  It  is 
argued  that  the  iron  could  have  absorbed  these  gases  only  when 
immersed  in  a  hot  dense  atmosphere  saturated  with  them,  —  a 
condition  existing,  so  far  as  known,  only  on  the  sun  and  stars. 

An  investigation  by  the  late  Professor  Newton,  however, 
shows  that  about  ninety  per  cent  of  the  aerolites,  for  the  deter- 
mination of  whose  orbits  we  have  sufficient  data,  were  moving 
around  the  sun  before  their  encounter  with  the  earth  in  paths 
not  parabolic,  but  resembling  those  of  the  short-period  comets, 
or  more  eccentric  asteroids,  and  nearly  all  direct,  suggesting  a 
planetary  rather  than  a  stellar  origin;  they  might  possibly  be 
minute  outriders  of  the  asteroid  family. 

Lord  Kelvin  suggested  many  years  ago  that  meteors  may 
have  acted  in  conveying  germs  of  life  from  one  part  of  the 


METEORS   AND   SHOOTING-STARS  463 

universe  to  another, — :a  suggestion,  however,  not  generally  Theory  of 
accepted,  since  they  seem  to  have  passed  through  conditions  friers  of* 
of  temperature  which  must  have  destroyed  all  life.  life  im- 

514.  Number  of  the  Aerolites.  —  As  to  the  number  of  these  Probable- 
bodies  which  strike  the  earth,  it  is  difficult  to  make  a  trustworthy 
estimate.     We  generally  add  to  our  cabinets  each  year  speci- 
mens of  from  two  to  six  meteors  which  have  been  seen  to  fall. 

But  for  one  that  is  found,  even  of  the  meteors  whose  flight  has  Number  of 
been  observed,  a  dozen  are  missed ;  and  if  we  include  all  that  aerolltes- 
were  not  seen,  or  that  fell  unobserved  on  the  ocean  or  in  regions 
from  which  no  report  could  come,  the  sum  total  must  be  very 
great.     Schreibers  estimated  the  number  at  seven  hundred  a 
year.     Reichenbach  puts  it  at  three  or  four  thousand,  but  this 
is  probably  excessive. 

SHOOTING-STARS 

515.  Their  Nature  and  Appearance.  —  These  are   the  swift-  shooting- 
moving,  evanescent,  starlike  points  of  light  which  may  be  seen  stars: 
every  few  moments  on  any  clear  moonless  night.     They  make  J^nute  aero- 
no  sound,  nor  (perhaps  with  one  exception,  to  be  noted  later)  lites>  but 
has  anything  been  known  to  reach  the  earth's  surface  from  ™ouds!  ° 
them,  not  even  in  the  greatest  "  meteoric  showers." 

For  this  reason  it  may  be  well  to  retain  provisionally  the  old 
distinction  between  them  and  the  large  meteors  from  which  aero- 
lites fall.  It  is  quite  probable  that  the  distinction  has  no  real 
ground,  that  shooting-stars  are  just  like  other  meteors,  except 
in  size,  being  so  small  that  they  are  entirely  consumed  in  the 
air;  but  then,  on  the  other  hand,  there  are  some  things  which 
favor  the  idea  that  the  two  classes  of  bodies  differ  in  constitu- 
tion about  as  asteroids  do  from  comets. 

516.  Number  of  Shooting-Stars.  —  Their  number  is  enormous. 
A  single  ordinary  observer  averages  from  four  to  eight  an  hour ; 
one  used  to  observation^  well  situated  and  on  a  moonless  night, 


464 


MANUAL   OF   ASTKONOMY 


Their  num- 
ber ten  to 
twenty  mil- 
lion daily. 


Average 
hourly  num- 
ber in  morn- 
ing twice  as 
great  as  in 
evening. 


Determina- 
tion of 
path,  etc. 


will  see  at  least  twice  as  many;  Schmidt  of  Athens  sets  the 
average  number  at  fourteen.  If  the  observers  are  sufficiently 
numerous  and  so  organized  as  to  be  sure  of  noting  all  that  are 
visible  from  their  station,  about  eight  times  as  many  will  be 
counted. 

On  this  basis  Professor  Newton  has  estimated  that  the  total 
number  which  enter  our  atmosphere  daily  must  be  between 
ten  and  twenty  million,  the  average  distance  between  them 
being  over  200  miles;  and  besides  those  which  are  visible  to 
the  naked  eye  there  is  an  immensely  larger  number  so  small  as 
to  be  observable  only  with  the  telescope.  Dr.  See  estimates 
the  number  of  these  as  at  least  one  hundred  million  daily. 

The  average  hourly  number  about  six  o'clock  in  the  morning 
is  double  the  hourly  number  in  the  evening,  and  the  meteors 
move  much  swifter,  the  reason  being  that  in  the  morning  we 
are  on  the  front  of  the  earth  as  regards  its  orbital  motion,  while 
in  the  evening  we  are  in  the  rear.  (The  earth's  orbital  motion 
is  always  directed  towards  a  point  on  the  ecliptic  about  90°  west 
of  the  sun.)  In  the  evening,  therefore,  we  see  only  such  as 
overtake  us.  In  the  morning  we  see  all  that  we  either  meet  or 
overtake.  This  proportion  of  morning  and  evening  meteors 
is  precisely  what  it  should  be  if  they  come  to  us  indiscrimi- 
nately from  all  directions  and  with  the  parabolic  velocity  of 
26  miles  a  second. 

517.  Elevation,  Path,  and  Velocity, —  By  observations  made 
at  stations  30  or  40  miles  apart  (best  by  photography)  it  is  easy 
to  determine  these  data  with  some  accuracy  whenever  meteors 
identifiable  at  the  two  or  more  stations  make  their  appearance. 
It  is  found  that  on  the  average  the  shooting-stars  appear  at 
a  height  of  about  74  miles  and  disappear  at  an  elevation  of 
about  50  miles,  after  traversing  a  course  of  40  or  50  miles,  with 
a  velocity  of  from  10  to  30  miles  a  second,  —  about  25  on  the 
average.  They  do  not  begin  to  be  visible  at  so  great  a  height 
as  the  aerolitic  meteors,  and  they  are  more  quickly  consumed 


METEORS   AND   SHOOTING-STARS  465 

and  therefore  do  not  penetrate  our  atmosphere  to  so  great  a 
depth, — fortunately  for  us. 

518.  Brightness,  Material,  etc. — Now  and  then  a  shooting-  Brightness, 
star  rivals  Jupiter  or  even  Venus  in  brightness.     A  consider- 
able number  are  like  first-magnitude  stars,  but  the  great  majority 

are  faint.     The  bright  ones  generally  leave  trains,  which  some-  Trains, 
times  endure  from  five  to  ten  minutes  and  then  fold  up  and 
are  wafted  away  by  the  air  currents,  which  at  40  miles  above 
the  earth's  surface  ordinarily  have  velocities  of  from  50  to  75 
miles  an  hour. 

The  swift  meteors  are  usually  of  green  or  bluish  tinge,  while  Color, 
those  that  move  slowly  are  generally  red  or  yellow. 

Occasionally  it  has  been  possible  to  get  a  "  snap  shot,"  so  to 
speak,  at  the  spectrum  of  a  meteor,  and  in  it  the  bright  lines  Spectrum. 
of  sodium   and  (probably)   magnesium  are  fairly  conspicuous 
among  many  others  which  cannot  be  identified  by  a  hasty  glance. 

Since  these  bodies  are  consumed  in  the  air,  all  we  can  hope 
to  get  of  their  material  is  their  ashes.  In  most  places  its  collec-  Meteoric 
tion  and  identification  is  hopeless;  but  Nordenskiold  thought  ashes- 
that  it  might  be  found  in  the  polar  snows.  In  Spitzbergen  he 
therefore  melted  several  tons  of  snow,  and  on  filtering  the  water 
he  actually  detected  in  it  a  sediment  containing  minute  globules 
of  oxid  and  sulphid  of  iron.  Similar  globules  have  also  been 
found  in  the  products  of  deep-sea  dredging.  They  may  be 
meteoric ;  but  what  we  now  know  of  the  distance  to  which  smoke 
and  fine  volcanic  dust  is  carried  by  the  wind  makes  it  not 
impossible  that  they  may  be  of  purely  terrestrial  origin. 

519.  Probable  Mass  of  Shooting-Stars.  —  We  have  no  way  probable 
of  determining  the  exact  mass  of  such  a  body;  but  from  the  massex- 

,.    -,  ,  ,.  tremely 

light  it  emits,  as  seen  from  a  known  distance,  an  estimate  can  smaii. 
be  formed  not  likely  to  be  widely  erroneous. 

A  good  ordinary  incandescent  lamp  consumes  about  150  foot- 
pounds of  energy  per  minute  for  each  candle-power.  Assum- 
ing for  the  moment  that  the  ratio  of  the  total  light  emitted 


466 


MANUAL   OF   ASTRONOMY 


(luminous  energy)  to  the  total  energy  consumed  is  the  same  for 
a  meteor  as  for  an  electric  lamp,  we  can  compute  the  total 
energy  of  a  meteor  which  shines  with  known  brightness  for  a 
given  time  at  a  known  distance. 

Suppose,  for  instance,  that  the  shooting-star  is  at  an  average 
distance  during  its  flight  of  30  miles  from  the  observer  and 
appears  as  bright  as  a  16  candle-power  lamp  ^  of  a  mile  away, 
and  shines  for  five  seconds  (^  minute).  The  total  luminous 
energy  then  equals 

150  x  16  x  TV  X         Y=  2  880000  foot-pounds. 


Suppose  its  velocity,  V,  to  be  20  miles,  or  105600  feet,  per 
second.  For  the  energy,  E,  in  foot-pounds,  of  a  moving  body 
whose  velocity  is  V  feet  per  second  and  its  mass  in  pounds  M, 
we  have 


M  V2 
- 


E 
(nearly),  whence,  M  =  64  x 


Finally,  then,  in  the  case  before  us, 

2880000       1  _,. 

1Q56QQ2  =  61  Pounds'  or  115  grams  (nearly). 

This  represents  fairly  the  observed  conditions  for  a  very 
bright  shooting-star. 

If  a  meteor  converted  all  its  energy  into  light,  —  i.e.,  if  its 
luminous  efficiency  were  higher  than  that  of  a  lamp,  —  this 
would  give  the  mass  much  too  great.  On  the  other  hand,  if 
the  meteor  were  only  feebly  luminous,  the  mass  thus  determined 
would  be  much  too  small. 

It  seems  likely  that  an  average  meteor  and  a  good  electric 
lamp  do  not  differ  widely  in  their  luminous  efficiency,  and 
on  this  basis  observations  indicate  that  ordinary  shooting-stars 
weigh  only  a  fraction  of  an  ounce,  —  from  a  grain  or  two  up  to 
100  or  150  grains.  Some  authorities,  however,  estimate  the 
mass  considerably  higher.  It  all  turns  on  the  assumed  "lumi- 
nous efficiency  "  of  the  shooting-stars. 


METEORS  AND   SHOOTING-STARS  467 

520.   Effects  produced  by  Meteors  and  Shooting-Stars.  —  (1)  Effects  due 
Meteors  add  continually  to  the  mass  of  the  earth.     If  we  assume  to  fal1  ?f 

meteoric 

20  000000  a  day,  each  weighing  ^  of  a  pound,  the  total  amount  matter 
would  be  about  50000  tons  a  year;  and  if  the  specific  gravity  practically 

_     ,  ,  .      insensible. 

of  the  meteoric  dust  averages  the  same  as  that  of  granite,  it 
would  take  about  eight  hundred  million  years  for  the  deposi- 
tion of  a  layer  1  inch  thick  on  the  earth's  surface. 

(2)  They  diminish  the  length  of  the  year  in  three  ways :  (a)  by 
acting  as  a  resisting  medium,  and  so  really  shortening  the  major 
axis  of  the  earth's  orbit  (just  as  the  orbit  of  Encke's  comet  is 
shortened) ;  (b)  by  increasing  the  mass  of  the  earth  and  sun,  and 
so  increasing  the  attraction  between  them;  (c)  by  increasing 
the  size  of  the  earth,  thus  slackening  its  rotation,  lengthening 
the  day,  and  so  making  fewer  days  in  the  year. 

Calculation  shows,  however,  that  on  the  preceding  assump- 
tion as  to  the  mass  of  the  meteors,  the  combined  effect  would 
hardly  amount  to  more  than  y^7  of  a  second  in  a  million  years. 

(3)  Each  meteor  brings  to  the  earth  a  certain  amount  of  heat, 
developed  in  the  destruction  of  its  motion.     According  to  the 
best  estimates,  however,  all  the  meteors  that  fall  upon  the  earth 
in  a  year  supply  no  more  heat  than  the  sun  does  in  about  one 
tenth  of  a  second. 

(4)  They  must  necessarily  render  space  imperfectly  transparent 
if  they  pervade  it  throughout  in  any  such  numbers  as  in  the 
domain  of  the  solar  system;  but  this  effect,  though  doubtless 
real,  is  also  so  small  as  at  present  to  defy  calculation. 


METEORIC  SHOWEES 

521.   There  are  occasions  when  the  shooting-stars,  instead  of  Meteoric 
appearing  here  and  there  in  the   sky  at  intervals  of  several  snowers- 
minutes,  appear  in  showers  of  thousands;  at  such  times  they 
do  not  move  at  random,  but  all  their  paths  diverge  or  radiate 
from  a  single  point  in  the  sky,  known  as  the  Radiant;  i.e.,  The  radiant 


468 


MANUAL    OF   ASTRONOMY 


Nomencla- 
ture of 
meteoric 
showers 


their  paths  produced  backward  all  pass  through  or  near  that 
point,  though  they  do  not  usually  start  there.  Meteors  which 
appear  near  the  radiant  are  apparently  stationary,  or  describe 
paths  which  are  very  short,  while  those  in  the  more  distant 
regions  of  the  sky  pursue  longer  courses. 

The  radiant  keeps  its  place  among  the  stars  sensibly  unchanged 
during  the  whole  continuance  of  the  shower,  —  for  hours  or  days, 
it  may  be,  —  and  the  shower  is  named  according  to  the  place  of 


The  radiant 

an  effect  of 

perspective. 


FIG.  170.  —  The  Meteoric  Radiant  in  Leo,  Nov.  13,  1866 

the  radiant  among  the  constellations.  Thus,  we  have  the  Leo- 
nids, or  meteors  whose  radiant  is  in  the  constellation  of  Leo, 
the  Andromedes  (or  Bielids),  the  Perseids,  the  Lyrids,  etc. 

Fig.  170  represents  the  tracks  of  a  large  number  of  the  Leonids  of  1866, 
showing  the  position  of  the  radiant  near  £  Leonis.  It  shows  also  the 
tracks  of  four  meteors  observed  during  the  same  time,  which  did  not 
belong  to  the  shower. 

The  radiant  is  a  mere  effect  of  perspective.     The  meteors  are 

. 

a^  moving  in  lines  nearly  parallel  when  encountered  by  the 


METEORS   AND   SHOOTING-STARS  469 

earth,  and  the  radiant  is  simply  the  perspective  vanishing  point 
of  this  system  of  parallels ;  their  paths  all  appear  to  converge, 
like  the  rails  of  a  railway  track  for  an  observer  looking  upon 
it  from  a  bridge.  The  position  of  the  radiant  on  the  celestial 
sphere  depends  entirely  upon  the  direction  of  the  motion  of  the 
meteors  relative  to  the  observer.  For  various  reasons,  however, 
the  paths  of  the  meteors,  on  account  of  irregularities  in  their 
form  and  surfaces,  are  not  exactly  parallel  or  straight,  and  in 
consequence  the  radiant  is  not  a  mathematical  point,  but  a  spot 
or  patch  in  the  sky,  often  covering  an  area  of  3°  or  4°. 

Probably  the  most  remarkable  of  all  the  meteoric  showers 
that  have  ever  occurred  was  that  of  the  Leonids,  on  November 
12,  1833.     The  number  at  some  stations  was  estimated  as  high  The  Leonid 
as  200000  an  hour  for  five  or  six  hours.     "  The  sky  was  as  full  shower  of 
of  them  as  it  ever  is  of  snowflakes  in  a  storm  "  and,  as  an  old 
lady  described  it,  looked  "like  a  gigantic  umbrella." 

522.    Dates  of  Meteoric  Showers.  —  Meteoric  showers  are  evi-  Fixed  dates 
dently  caused  by  the  earth's  encounter  with  a  swarm  of  the  of  meteonc 

J         .  showers. 

little  bodies,  and  since  this  swarm  or  flock  pursues  a  regular 
orbit  around  the  sun,  the  earth  can  meet  it  only  when  she  is 
at  the  point  where  her  orbit  cuts  the  path  of  the  meteors ;  this, 
of  course,  must  always  happen  at  or  near  the  same  time  of  the 
year,  except  as  in  the  process  of  time  the  meteoric  orbits  shift 
their  positions  on  account  of  perturbations.  The  Leonid 
showers,  therefore,  appear  about  November  15,  and  the  Andro- 
medes  about  the  24th ;  but  both  dates  are  slowly  changing,  the 
Leonids  coming  gradually  later  and  the  Andromedes  earlier. 
Since  1800  the  former  have  shifted  from  November  12  to  the 
15th,  and  the  latter  from  the  28th  to  the  24th  since  18Y2. 

In  some  cases  the  meteors  are  distributed  along  their  whole  Annual  re- 
orbit,  forming  a  sort  of  ring  and  rather  widely  scattered.     In 
that  case  the  shower  recurs  every  year  and  may  continue  for 
several  weeks,   as  is  the    case  with  the   Perseids,   or  August 
meteors.     On  the  other  hand,  the  flock  may  be  concentrated, 


470 


MANUAL   OF   ASTRONOMY 


and  then  a  notable  shower  will  occur  only  on  the  day  when  the 
earth  and  the  meteors  arrive  together  at  the  orbit  crossing. 
This  is  the  case  with  both  the  Leonids  and  the  Andromedes, 
though  the  latter  are  already  getting  pretty  widely  scattered. 
The  showers  then  occur,  not  every  year,  but  only  at  intervals 
of  several  years,  and  always  on  or  near  the  same  time  of  the 
month.  For  the  Leonids  the  interval  is  about  thirty-three 
years,  and  for  the  Andromedes  usually  thirteen,  but  sometimes 
only  six  or  seven. 

The  meteors  which  belong  to  the  same  group  have  certain 
family  resemblances.  The  Perseids  are  yellow  and  move  with 
medium  velocity.  The  Leonids  are  very  swift  (we  meet  them), 
and  they  are  of  a  bluish  green  tint,  with  vivid  trains.  The 
Andromedes  are  sluggish  (they  overtake  the  earth),  are  reddish, 
being  less  intensely  heated  than  the  others,  and  usually  have 
only  feeble  trains. 

About  one  hundred  meteoric  radiants  are  now  recognized  and  cata- 
logued. The  most  conspicuous  of  them,  except  those  already  named, 
are  the  following:  the  Draconids,  January  2;  Lyrids,  April  20;  Aqua- 
riids  7,  May  6  ;  Aquariids  II,  July  28  ;  Orionids,  October  20  ;  Geminids, 
December  10. 

523,  Stationary  Radiants.  —  When  a  meteoric  shower  per- 
sists for  days  and  even  weeks,  as  do  the  Perseids  for  instance, 
the  radiant,  as  a  rule,  gradually  shifts  its  position  among  the 
stars,  on  account  of  the  change  in  the  direction  of  the  earth's 
motion,  —  as  it  ought  to,  since  the  place  of  the  radiant  depends 
upon  the  combination  of  the  earth's  motion  with  that  of  the 
meteors. 

Mr.  Denning  of  Bristol  (England),  for  many  years  an  assid- 
uous observer  of  meteors,  claims,  however,  to  have  discovered 
numerous  cases  in  which  the  radiant  of  a  long-continued  shower 
remains  absolutely  stationary;  and  he  presents  as  typical  the 
Orionids,  which  scatter  along  from  about  October  10  to  24,  all 


METEORS   AND    SHOOTING-STARS  471 

the  time,  according  to  his  observations,  keeping  their  radiant 
close  to  the  star  v  Orionis. 

No  satisfactory  explanation  of  such  fixity  of  the  radiant  yet  Difficult  to 
appears,  though  certain  mathematical  investigations  by  Turner  exPlam- 
of  Oxford  (on  the  disturbing  effect  of  the  earth  upon  meteors 
passing  near  her)  look  promising  and  may  resolve  the  problem; 
but  some  high  authorities  still  remain  skeptical  as  to  the  fact. 

524.  The  Mazapil  Meteorite.  —  As  has  been  said,  during  these  Meteorite 
showers  no  sound  is  heard,  no  sensible  heat  perceived,  nor  have  ^^ fel1 
any  masses  ever  reached  the  ground;  with  the  one  exception,  shower  of 
however,  that  on  Nov.  27,  1885,  a  piece  of  meteoric  iron  fell  at  Bielids« 
Mazapil,  in  northern  Mexico,  during  the  shower  of  Andromedes, 

or  "  Bielids,"  which  occurred  that  evening. 

Whether  the  coincidence  was  accidental  or  not,  it  is  inter- 
esting. Many  high  authorities  speak  confidently  of  this  piece 
of  iron  as  being  a  piece  of  Biela's  comet  itself. 

This  brings  us  to  one  of  the  most  remarkable  discoveries  of 
nineteenth-century  astronomy. 

CONNECTION  BETWEEN  COMETS  AND  METEOKS 

525.  At  the  time  of  the  great  meteoric  shower  of  1833,  Pro-  oimsted's 
fessors  Olmsted  and  Twining  of  New  Haven  were  the  first  to  rec°snition 

of  meteoric 

recognize  the  radiant  and  to  point  out  its  significance  as  indi-  swarms  as 
eating  the  existence  of  a  swarm  of  meteors  revolving  around  cometlike- 
the  sun  in  a  permanent  orbit ;  Olmsted  even  went  so  far  as  to 
call  the  body  a  "  comet."     Others  soon  showed  that,  in  some 
cases  at  least  (Perseids),  the  meteors  must  be  distributed  in  a 
complete  ring  around  the  sun,  and  Erman  of  Berlin  developed 
a  method  of  computing  the  meteoric  orbit  when  its  radiant  is 
known. 

In  1864  Professor  Newton  of  New  Haven  showed  by 
an  examination  of  the  old  records  that  there  had  been  a 
number  of  great  meteoric  showers  in  November,  at  intervals  of 


472 


MANUAL   OF   ASTRONOMY 


Newton's 
prediction 
of  shower 
of  1866. 


Failure  in 
1900. 


Second 
shower  of 
1901. 


Cause  of 
failure  in 
1900. 


thirty-three  or  thirty-four  years,  and  he  predicted  confidently  a 
repetition  of  the  shower  on  Nov.  13  or  14,  1866.  The  shower 
occurred  as  predicted  and  was  observed  in  Europe ;  and  it  was 
followed  by  another  in  1867,  which  was  visible  in  America,  the 
meteoric  swarm  being  extended  in  so  long  a  procession  as  to 
require  more  than  two  years  to  cross  the  earth's  orbit.  Neither 
of  these  showers,  however,  was  equal  to  the  shower  of  1833. 
The  researches  of  Hewton,  supplemented  by  those  of  Adams, 
the  discoverer  of  Neptune,  showed  that  the  swarm  moves  in  a 
long  ellipse  with  a  thirty-three-year  period. 

A  return  of  the  shower  was  expected  in  1899  or  1900,  but 
failed  to  appear,  though  on  Nov.  14-15,  1898,  a  considerable 
number  of  meteors  were  seen,  and  in  the  early  morning  of 
Nov.  14-15,  1901,  a  well-marked  shower  occurred,  visible  over 
the  whole  extent  of  the  United  States,  but  best  seen  west  of  the 
Mississippi,  and  especially  on  the  Pacific  coast.  At  a  number 
of  stations  several  hundred  Leonids  were  observed  by  eye  or  by 
photography,  and  the  total  number  that  fell  must  be  estimated 
by  tens  of  thousands.  The  display,  however,  seems  to  have 
nowhere  rivaled  the  showers  of  1866-67,  and  these  were  not  to 
be  compared  with  that  of  1833.  Very  few  meteors  were  seen  in 
1902,  but  in  1903  a  large  number  were  observed  in  Greece  and 
in  England. 

The  calculations  of  Downing  and  Stoney  show  that  the  failure  in  1900 
was  probably  due  to  perturbations  of  the  meteors  by  the  action  of  Jupiter, 
Saturn,  and  Uranus  during  their  absence  from  the  neighborhood  of  the 
sun,  causing  the  main  body  to  pass  at  a  distance  of  nearly  2  000000  miles 
below  the  orbit  of  the  earth. 


Schiapa-  526.    Identification  of  Meteoric  Orbits  with  Cometary.  —  The 

reiii'sidenti-  researches  of  Newton  and  Adams  had  awakened  lively  interest 

orbit  of         in  the  subject,  and  Schiaparelli,  a  few  weeks  after  the  Leonid 

Perseids.        shower,  published  a  paper  upon  the  Perseids,  or  August  meteors, 

in  which  he  brought  out  the  remarkable  fact  that  they  are 


METEORS   AND   SHOOTING-STARS  473 

moving  in  the  same  orbit  as  that  of  the  bright  comet  of  1862, 
known  as  Tuttle's  comet.    Shortly  after  this  Leverrier  published 
his  orbit  of  the  Leonid  meteors,  derived  from  the  observed  posi- 
tion of  the  radiant  in  connection  with  the  periodic  time  assigned  Leverrier 
by  Adams  ;  and  almost  simultaneously,  but  without  any  idea  and  Op~ 
of  a  connection  between  them,  Oppolzer  published  his  orbit  of  orbit  of 

Leonids, 


FIG.  171.  —  Orbits  of  Meteoric  Swarms 

Tempel's  comet  of  1866,  and  the  two  orbits  were  at  once  seen 
to  be  practically  identical.  Now  a  single  coincidence  might  be 
accidental,  but  hardly  two. 

Five  years  later  came  the  shower  of  the  Andromedes,  follow-  Andromedes 
ing  in  the  track  of  Biela's  comet,  and  among  more  than  one  andBiela's 

t     .  comet. 

hundred  of  the  distinct  meteor  swarms  now  recognized  Prof. 
Alexander  Herschel  finds  five  others  which  are  similarly  related 
each  to  its  special  comet.  It  is  no  longer  possible  to  doubt 
that  there  is  a  real  and  close  connection  between  these  meteors 
and  their  attendants.  Fig.  171  represents  four  of  these  cometo- 
meteoric  orbits. 


474 


MANUAL   OF   ASTRONOMY 


Nature  of 
connection 
between 
comets  and 
meteors  not 
yet  deter- 
mined. 


Transforma- 
tion of 
meteoric 
swarm  into 
a  ring. 


Rings  older 
than  com- 
pact 
swarms. 


The  mete- 
oritic  hy- 
pothesis. 


527.  Nature  of  the  Connection.  —  This  cannot  be  said  to  be 
ascertained.  In  the  case  of  the  Leonids  and  the  Andromedes 
the  meteoric  swarm  follows  the  comet,  but  this  does  not  seem  to 
be  so  in  the  case  of  the  Perseids,  which  scatter  along  more  or 
less  abundantly  every  year. 

The  prevailing  belief  at  present  seems,  on  the  whole,  to  be 
that  the  comet  itself  is  only  the  thickest  part  of  a  meteoric 
swarm,  and  that  the  clouds  of  meteors  scattered  along  its  path 
result  from  its  disintegration. 

It  is  easy  to  show  that  if  a  comet  really  is  such  a  swarm  it  is 
likely  to  break  up  gradually  more  and  more  at  each  return  to 
perihelion,  and  at  every  near  approach  to  one  of  the  larger 
planets,  dispersing  its  constituent  particles  along  its  path  until 
the  compact  swarm  has  become  a  diffuse  ring.  The  different 
parts  of  the  comet  are  at  different  distances  from  the  sun,  and 
there  is  almost  no  sensible  mutual  attraction  between  them, 
the  mass  is  so  minute.  The  attraction  of  the  sun  or  planet  is 
therefore  likely  to  cause  the  separation  that  has  been  referred  to. 

The  longer  the  comet  has  been  moving  around  the  sun,  the 
more  uniformly  the  particles  will  be  distributed.  The  Perseids 
are  supposed,  therefore,  to  have  been  in  the  system  for  a  long 
time,  while  the  Leonids  and  Andromedes  are  believed  to  be 
comparatively  new-comers.  Leverrier,  indeed,  has  gone  so  far 
as  to  indicate  the  year  A.D.  126  as  the  time  at  which  Uranus 
captured  Tempel's  comet  and  brought  it  into  the  system  (as 
illustrated  by  Fig.  172).  But  the  theory  that  meteoric  swarms 
are  the  product  of  cometary  disintegration  assumes  that  comets 
are  compact  aggregations  when  they  enter  the  system,  which  is 
by  no  means  certain. 

528.  Sir  Norman  Lockyer's  Meteoritic  Hypothesis.  —  Within 
the  last  twenty  years  Sir  Norman  Lockyer  has  been  enlarging 
greatly  the  astronomical  importance  of  meteors.  The  probable 
meteoric  constitution  of  the  zodiacal  light,  as  well  as  of  Saturn's 
rings,  and  of  the  comets,  has  long  been  recognized ;  but  he  goes 


METEORS   AND   SHOOTING-STARS 


475 


much  further  and  maintains  that  all  the  heavenly  bodies  are 
either  meteoric  swarms,  more  or  less  condensed,  or  the  final 
products  of  such  condensation.  Upon  this  hypothesis  he 
attempts  to  explain  the  evolution  of  the  planetary  system,  the 
phenomena  of  temporary  and  variable  stars,  the  various  classes 


FIG.  172.  —  Origin  of  the  Leonids 

of  stellar  spectra,  the  forms  and  structure  of  the  nebulae,  —  in 
fact,  pretty  much  everything  in  the  heavens  from  the  aurora 
borealis  to  the  sun.  As  a  working  hypothesis  his  theory  is 
unquestionably  suggestive  and  has  attracted  much  attention, 
but  it  encounters  serious  difficulties  in  details  and  cannot  be 
said  to  be  as  yet  "  accepted." 


476 


MANUAL   OF   ASTRONOMY 


EXERCISES 

1.  If  a  compact  swarm  of  meteors  were  now  to  enter  the  system  and  be 
deflected  by  the  attraction  of  some  planet  into  an  elliptical  orbit  around 
the  sun,  would  the  swarm  continue  to  be  compact  ?     If  not,  what  would  be 
the  ultimate  distribution  of  the  meteors  ? 

2.  What  is  the  probable  relative  age  of  meteoric  swarms  and  meteoric 
rings  as  members  of  the  solar  system  ? 

3.  Assuming  that  the  earth  encounters  20  000000  meteors  every  24 
hours,  what  is  the  average  number  in  a  cubic  space  of  1000  000000  cubic 
miles  (i.e.,  a  cube  1000  miles  on  each  edge)?  Ans.    About  250. 

4.  If  space  were  occupied  by  meteors  uniformly  distributed  100  miles 
apart  on  three  sets  of  lines  perpendicular  to  each  other,  how  many  would 
be  encountered  by  the  earth  in  a  day  ?  Ans.   78700000. 

NOTE.  —  In  this  cubical  arrangement  the  average  distance  between  the  meteors 
much  exceeds  100  miles.  If  they  were  packed  as  closely  as  possible,  consistently 
with  the  condition  that  the  distance  between  two  neighbors  should  nowhere  be  less 
than  100  miles,  the  number  would  be  increased  by  nearly  forty  per  cent. 


Lick  Observatory 


CHAPTER    XVIII 
THE   STARS 

Their  Nature,  Number,  and  Designation  —  Star-Catalogues  and  Charts  —  The  Photo- 
graphic Campaigns  —  Proper  Motions,  Radial  Motions,  and  the  Motion  of  the 
Sun  in  Space  —  Stellar  Parallax 

529.  Our  solar  system  is  an  island  in  space,  surrounded  by  The  solar 
an  immense  void  inhabited  only  by  meteors  and  comets.  If  8ysteman 

*       J  island  in 

there  were  any  body  a  hundredth  part  as  large  as  the  sun  within  space, 
a  distance  of  a  thousand  astronomical  units,  its  presence  would 
be  indicated  by  disturbances  of  Uranus  and  Neptune,  even  if  it 
were  itself  invisible. 

The  nearest  star,  so  far  as  known  at  present,  is  at  a  distance  Distance  of 
of  more  than  275000  astronomical  units,  —  so  remote  that,  seen  E 
from  it,  our  sun  would  look  about  like  the  pole-star,  and  no 
telescope  ever  yet  constructed  would  be  able  to  show  a  single 
one  of  all  the  planets  of  the  solar  system. 

That  the  stars  are  suns,  i.e.,  bodies  of  the  same  nature  The  stars 
as  our  own  sun,  composed  largely  of  the  same  substances  ^  Differ 
and  under  similar  physical  conditions,  is  shown  by  their  spec-  greatly  in 
tra.  Each  star  has  its  incandescent  photosphere  surrounded  slzeand 

i  i  11-1-  ^  ^    -      intrinsic 

by  a  gaseous  envelope,  and  while  in  a  general  way  their  brilliance, 
spectra  resemble  each  other  as  human  faces  do,  each  has  its 
own  peculiarities  ot  detail.  Small  as  they  appear  to  us,  they 
are  many  of  them  immensely  larger  and  hotter  than  the  sun; 
others,  however,  are  smaller  and  cooler,  and  some  hardly  shine 
at  all.  They  differ  enormously  among  themselves  in  mass, 
bulk,  and  brightness,  not  being  as  much  alike  as  individuals 
of  a  single  race  usually  are,  but  differing  as  widely  as  whales 
from  minnows. 

477 


4T8 


MANUAL   OF  ASTRONOMY 


Number 
visible  to 
the  naked 
eye. 


530.  Number  of  the   Stars.  —  Those  that  are  visible  to  the 
eye,  though   numerous,   are  by  no   means   countless.      If  we 
examine  a  limited  region,  as,  for  instance,  the  bowl  of  "The 
Dipper,"  we  shall  find  that  the  number  we  can  see  within  it  is 
not  very  large, — hardly  a  dozen,  even  on  a  very  dark  night. 

In  the  whole  celestial  sphere  the  number  of  stars  bright 
enough  to  be  distinctly  seen  by  an  average  eye  is  between 
six  and  seven  thousand,  and  that  only  in  a  perfectly  clear 
and  moonless  sky;  a  little  haze  or  moonlight  will  cut  down 
the  number  by  fully  one  half.  At  any  one  time  not  more  than 
two  thousand  or  twenty-five  hundred  are  fairly  visible,  since,  of 
course,  one  half  are  below  the  horizon  and  near  it  the  small 
stars  (which  are  vastly  the  most  numerous)  disappear.  The 
total  number  which  could  be  seen  by  the  ancient  astronomers 
well  enough  to  be  observable  with  their  instruments  is  not  quite 
eleven  hundred. 

With  even  the  smallest  telescope  the  number  is  enormously 
increased.  A  common  opera-glass  brings  out  at  least  one  hun- 
dred thousand,  and  with  a  2^-inch  telescope  Argelander  made 
his  Durchmusterung  of  stars  north  of  the  equator,  three  hun- 
dred and  twenty-four  thousand  in  number.  The  Yerkes  tel- 
escope, 40  inches  in  diameter,  probably  reaches  over  one 
hundred  million. 

531.  Constellations.  —  -  The    stars    are    grouped   in   so-called 
"constellations,"  many  of  which  are  extremely  ancient,  all  those 
of  the  zodiac  and  all  those  near  the  northern  pole  being  of  pre- 
historic origin.    Their  names  are,  for  the  most  part,  drawn  from 
the   Greek  and  Roman  mythology,  many  of  them  being  con- 
nected in  some  way  or  other  with  the  Argonautic  expedition. 

In  some  cases  the  eye,  with  the  help  of  a  lively  imagination, 
can  trace  in  the  arrangement  of  the  stars  a  vague  resemblance 
to  the  object  which  gives  name  to  the  constellation,  as  in  the 
case  of  Draco  for  instance,  but  generally  no  reason  is  obvious 
for  either  name  or  boundaries. 


THE   STARS  479 

Of  the  sixty-seven  constellations  now  generally  recognized,  forty-eight   Sixty-seven 
have  come  down  from  Ptolemy,  the  others  having  been  formed  since  1600   now  recog- 
by  later  astronomers,  in  order  to  embrace  stars  not  included  in  the  old   nized : 
constellations,  and  especially  to  provide  for  the  stars  near  the  southern   ptoiemaic 
pole.      Many   other  constellations   have  been   proposed   at   one  time  or 
another,  but  have  since  been  rejected  as  useless  or  impertinent,  though 
about  a  dozen  have  obtained  partial  acceptance  and  still  hold  a  place  upon 
some  star-maps. 

Originally  certain  stars  were  reckoned  as  belonging  to  more  Consteiia- 
than  one  constellation,  but  at  present  this  is  no  longer  the  case:  tlonbound- 

0  anes. 

the  entire  surface  of  the  celestial  sphere  is  divided  up  between 
recognized  constellations.  There  is,  however,  no  decisive  defi- 
nition of  their  respective  boundaries,  and  different  authorities 
disagree  at  many  points.  Argelander  is  now  generally  accepted 
as  the  authority  for  the  northern  constellations  and  Gould  for 
the  southern. 

A  thorough  knowledge  of  these  artificial  star  groups  and  of  the  names   Knowledge 
and  places  of  the  stars  that  compose  them  is  not  at  all  essential,  even  to  an   of  constella- 
accomplished  astronomer ;  but  it  is  a  matter  of  great  convenience  and  of 
real  interest  to  an  intelligent  person  to  be  acquainted  with  the  principal   not  essentiai 
constellations l   and   to   be    able   to   recognize   at   a  glance  the  brighter  to  an 
stars,  —  from  fifty  to  one  hundred  in  number.     This  amount  of  knowledge   astronomer, 
is  easily  obtained  in  a  few  evenings  by  studying  the  heavens  in  connec- 
tion with  a  good  celestial  globe  or  star-map,  taking  care,   of  course,  to 
select  evenings  in  different  seasons  of  the  year,  so  that  the  whole  sky  may 
be  covered. 

532,   Methods  of  designating  Individual  Stars.  —  (a)  By  Names.  Designation 
About  sixty  of  the  brighter  stars  have  names  in  more  or  less  ofstars:by 

names. 

common  use. 

1  In  his  Uranography,  a  booklet  of  about  fifty  pages,  published  by  Ginn  & 
Company,  the  author  has  given  a  brief  description  of  the  various  constellations 
and  directions  for  tracing  them.  The  star-maps  which  accompany  it  are  quite 
sufficient  for  this  purpose,  though  not  on  a  scale  large  enough  to  answer  for 
detailed  study.  For  reference  purposes,  Professor  Upton's  Star  Atlas  (issued 
by  the  same  publishers)  is  recommended,  or  Schurig's,  which  is  excellent  and 
very  cheap,  —  obtainable  from  dealers  in  foreign  books. 


480 


MANUAL   OF    ASTRONOMY 


A  majority  of  these  names  are  of  Greek  or  Latin  origin  (e.g., 
Capella,  Sirius,  Arcturus,  Procyon,  Regulus,  etc.);  others  have 
Arabic  names  (Aldebaran,  Vega,  Rigel,  Altair,  etc.).  For  the 
smaller  stars  the  names l  are  almost  entirely  Arabic. 

(b)  By  the  Star's  Place  in  the  Constellation.     This  was  the 
usual  method  employed  by  Ptolemy  and  Tycho  Brahe. 

Spica,  for  instance,  is  the  star  in  the  spike  of  wheat  which 
Virgo  carries ;  Cynosure  is  Greek  for  "  the  tail  of  the  dog  "  (in 
ancient  times  the  constellation  which  we  now  call  Ursa  Minor 
was  a  dog);  Capella  is  the  goat  which  Auriga,  the  charioteer, 
carries  in  his  arms.  Hipparchus,  Ptolemy,  in  fact  all  the 
older  astronomers,  including  Tycho  Brahe,  used  this  method  to 
indicate  particular  stars,  speaking,  for  instance,  of  "the  star 
in  the  head  of  Hercules,"  or  in  the  "  right  knee  of  Bootes  " 
(Arcturus). 

(c)  By  Constellation  and  Letter.     In  1603  Bayer,  in  publish- 
ing his  star-map,  adopted  an  excellent  plan,  ever  since  followed, 
of  designating  the  stars  in  a  constellation  by  the  letters  of 
fche  Greek  alphabet.     The  letters  generally  (not  always)  were 
applied  in  the  order  of  brightness,  a  being  the  brightest  star  of 
the  constellation  and  fi  the  next  brightest ;  but  they  are  some- 
times (as  in  the  case  of  "  The  Dipper  ")  assigned  to  the  stars  in 
their  order  of  position  rather  than  in  that  of  brightness. 

When  the  naked-eye  stars  of  a  constellation  are  so  numerous 
as  to  exhaust  the  letters  of  the  Greek  alphabet  the  Roman 
letters  are  next  used,  and  then,  if  necessary,  we  employ  num- 
bers which  Flamsteed  assigned  a  century  later. 

At  present  every  naked-eye  star  can  be  referred  to  and  iden- 
tified by  its  letter  or  Flamsteed  number  in  the  constellation  to 
which  it  belongs. 

1  Allen's  Star-Names  and  their  Meanings  (G.  E.  Stechert  Company,  New 
York)  is  the  best  work  on  the  subject ;  full  of  curious  and  interesting  informa- 
tion relating  to  the  names  themselves,  and  to  the  various  legends  connected  with 
them  and  with  the  constellations. 


THE   STARS  481 

(d)  By  Catalogue  Number.     The  preceding  methods  all  fail  By  number 
in  the  case  of  telescopic  stars.     To  such  we  refer  as  number  m  a  star~ 

*  catalogue. 

so-and-so  of  some  one's  catalogue;  thus,  "LI.,  21185  "  is  read 
"Lalande,  21185,"  and  means  the  star  so  numbered  in  Lalande's 
catalogue.  At  present  about  eight  hundred  thousand  different 
stars  are  contained  in  our  numerous  catalogues,  so  that  (except 
in  the  Milky  Way)  every  star  visible  in  a  3-inch  telescope  can 
be  found  and  identified  in  one  or  more  of  them. 

Synonyms.      Of  course  all  the  bright  stars  which  have  names  Synonyms, 
have  letters  also  and  are  sure  to  be  found  in  every  catalogue 
which  covers  their  part  of  the  heavens.     A  star  notable  for  any 
reason  has,  therefore,  usually  many  "  aliases,"  and  sometimes 
care  is  necessary  to  avoid  mistakes  on  this  account. 

533.   Star-Catalogues.  —  These  are  lists  of  stars,  arranged  in  Ancient  and 

medieval 
catalogues. 


some  regular  order,  giving  their  positions  (i.e.,  their  right  ascen-  medieval 


sions  and  declinations,  or  longitudes  and  latitudes),  and  usually 
also  indicating  their  so-called  magnitudes  or  brightness. 

The  first  of  these  star-catalogues  was  made  about  125  B.C.  by 
Hipparchus  of  Bithynia  (the  first  of  the  world's  great  astrono- 
mers), giving  the  longitude  and  latitude  of  1080  stars.  This 
catalogue  was  republished  by  Ptolemy  250  years  later,  the 
longitudes  being  corrected  for  precession,  though  not  quite 
correctly. 

The  next  of  the  old  catalogues  of  any  value  was  that  of 
Ulugh  Beigh,  made  at  Samarcand  about  A.D.  1450.  It  was 
followed  in  1580  by  the  catalogue  of  Tycho  Brahe,  containing 
1005  stars,  the  last  constructed  before  the  invention  of  the 
telescope. 

The  modern  catalogues  are  numerous,  —  already  counted  by 
the  hundred.     Some  give  the  places  of  a  great  number  of  stars 
rather  roughly,  merely  as  a  means  of  identifying  them  when 
used  for  cometary  observations  or  other  similar  purposes.     To  The 
this  class  belongs  Argelander's  Durchmusterung  of  the  northern  "  Durch- 
heavens,  which  contains  over  324000  stars,  —  the  largest  number  Ungs." 


482 


MANUAL   OF   ASTRONOMY 


Funda- 
mental 
Catalogues. 


Zones. 


The  Gesell- 
schaft  cata- 
logue. 


Funda- 
mental star 
places  de- 
termined by 
meridian- 
circle. 


Secondary 
places  by 
differential 
observa- 
tions. 


in  any  one  catalogue  thus  far  published.  This  has  since  been 
supplemented  by  Schoenfeld's  Southern  Durchmusterung,  on 
a  similar  plan. 

Then  there  are  the  "  Fundamental  Catalogues,"  like  the  Pul- 
kowa  and  Greenwich  catalogues,  which  give  the  places  of  a  few 
hundred  stars  only,  but  as  accurately  as  possible,  in  order  to 
furnish  reference  points  in  the  sky. 

The  so-called  "  Zones "  of  Bessel,  Argelander,  Gould,  and 
many  others  are  catalogues  covering  limited  portions  of  the 
heavens,  containing  stars  arranged  in  zones  about  a  degree 
wide  in  declination  and  running  through  some  hours  in  right 
ascension. 

An  immense  catalogue  is  now  in  process  of  publication  under 
the  auspices  of  the  German  Astronomische  Gesellschaft,  and 
will  contain  accurate  places  of  all  stars  above  the  ninth  mag- 
nitude north  of  15°  south  declination.  The  observations, 
by  numerous  cooperating  observatories,  have  occupied  twenty 
years,  but  are  at  last  finished,  and  very  nearly  all  of  the  dif- 
ferent parts  of  the  catalogue  are  already  published.  The  Cor- 
dova catalogue  and  Cordova  "  Zones,"  together  with  the  cata- 
logues and  Photographic  Durchmusterung  of  the  Cape  of  Good 
Hope  Observatory,  cover  the  rest  of  the  southern  heavens. 

534.  The  Determination  of  Star  Places  for  Catalogues The 

observations  from  which  a  star-catalogue  is  constructed  have 
until  lately  been  usually  made  with  the  meridian-circle.  For  the 
fundamental  catalogues  comparatively  few  stars  are  observed, 
but  all  with  the  utmost  care  and  on  every  possible  opportunity, 
during  several  years,  with  every  precaution  to  eliminate  all 
instrumental  and  observational  errors. 

In  the  more  extensive  catalogues  most  of  the  stars  have  been 
observed  only  two  or  three  times,  and  everything  is  made  to 
depend  upon  the  accuracy  of  the  places  of  the  "fundamental 
stars,"  which  are  assumed  as  correct.  The  instrument  in  this 
case  is  used  only  "  differentially  "  to  measure  the  comparatively 


THE   STARS  483 

small  difference  between  the  right  ascension  and  declination  of 
the  fundamental  stars  and  those  of  the  stars  to  be  catalogued. 

At  present,  by  means  of  photography,  the  catalogues  are  Photog- 
being  extended  to  stars  much  fainter  than  those  observable  by  iaP^now 
meridian-circles.     On  the  photographic  plates  the  positions  of 
the  smaller  stars  are  determined  by  reference  to  larger  stars 
which  appear  upon  the  same  plate,  and  the  catalogues  now  in 
process  of  construction  from  the  photographic  campaign  will 
contain  between  one  and  two  million  stars  down  to  the  eleventh 
magnitude. 

535.  Mean  and  Apparent  Places  of  the  Stars. — The  modern  Reduction 
star-catalogue  contains  the  mean  right  ascension  and  declination  °.f  mean 

place  to  ap- 

of  its  stars  at  the  beginning  of  some  designated  year,  i.e.,  the  parent  place 
place  the   star  would  occupy  on  that  date  if  there  were.no  andwce 

.     7  .  .  .          versa. 

equation  oj  the  equinoxes,  nutation,  aberration,  or  proper  motion. 
To  get  the  actual  (apparent)  right  ascension  and  declination  of 
a  star  for  some  given  date  (which  is  what  we  always  want  in 
practice),  the  catalogue  place  must  be  "reduced"  to  that  date, 
i.e.,  it  must  be  corrected  for  precession,  aberration,  etc.  The 
operation  with  modern  tables  and  formulae  is  not  a  very  tedious 
one,  involving  perhaps  five  minutes  work,  but  without  it  the 
catalogue  places  are  useless  for  accurate  purposes.  Vice  versa, 
the  observations  of  a  fixed  star  with  the  meridian-circle  do  not 
give  its  mean  right  ascension  and  declination  ready  to  go  into 
the  catalogue,  but  the  observations,  before  they  can  be  tabu- 
lated, must  be  reduced  backwards  from  the  apparent  place 
observed  to  the  mean  place  for  some  chosen  "  epoch." 

536,  Star  Charts  and  Stellar  Photography.  —  For  certain  pur-  star  charts, 
poses  accurate  star  charts  are  even  more  useful  than  catalogues. 

The  old-fashioned  way  of  making  such  charts  was  by  plotting 
the  results  of  zone  observations,  but  at  present  it  is  being  done, 
by  means  of  photography,  vastly  better  and  more  rapidly.     A  The  photo- 
cooperative  campaign  began  in  1889,  the  object  of  which  is  to  gra 
secure   a   photographic   chart   of   all   the  stars    down   to   the 


484 


MANUAL   OF   ASTRONOMY 


No  limit  yet 
found  to 
f  aintness  of 
stars  that 
can  be  pho- 
tographed. 


The  Paris 
photo- 
graphic tele- 
scope. 


fourteenth  magnitude.  The  work  is  now  more  than  three 
fourths  done.  Eighteen  different  observatories  have  participated 
in  the  work.  From  these  chart  plates  extensive  catalogues  are 
also  being  made,  as  already  mentioned. 

One  of  the  most  remarkable  things  about  the  photographic 
method  is  that  with  a  good  instrument  there  appears  to 

be  no  limit  to  the  faintness 
of  the  stars  that, can  be  photo- 
graphed; by  increasing  the 
time  of  exposure,  smaller  and 
smaller  stars  are  continually 
reached.  With  the  ordinary 
plates,  and  exposure  times  not 
exceeding  twenty  minutes,  it 
is  now  possible  to  get  distinct 
impressions  of  stars  that  the 
eye  cannot  possibly  see  with 
the  telescope  employed. 

Fig.  173  is  a  representation 
of  the  Paris  instrument  of  the 
Henry  Brothers,  which  was 
the  first  employed  in  such 
work  and  was  adopted  as  the 
typical  instrument  for  the 
FIG.  i73.-photographic  Telescope  of  the  chartingoperation.  It  has  an 

Pans  Observatory  r 

aperture   of   about  14   inches 

and  a  length  of  about  11  feet,  the  object-glass  being  specially 
corrected  for  the  photographic  rays.  A  9-inch  visual  telescope 
is  inclosed  in  the  same  tube,  so  that  the  observer  can  watch 
the  direction  of  the  instrument  during  the  whole  operation. 

The  instruments  used  at  the  other  observatories  differ  in 
mechanical  arrangements,  but  all  have  lenses  of  the  same 
aperture  and  focal  length,  the  scale  of  all  the  photographs  being 
1'  to  a  millimeter, — three  times  that  of  Argelander's  charts. 


THE   STARS  485 

As  already  mentioned,  these  charts  furnish  the  material  for  a 
very  extensive  catalogue. 

Several   other  very  large   photographic  telescopes  have  already  been   Other  large 
constructed.      The    Bruce    telescope,    presented    to    the    Harvard    College   photo- 
Observatory  by  the  late  Miss  Bruce  of  New  York,  has  for  its  objective  a  SraPhlc  tele- 
four-lens  photographic  doublet  2  feet  in  diameter,  but  with  a  focal  length 
of  only  11  feet,  —  the  same  as  those  mentioned  above,  —  so  that  its  nega- 
tives are  on  the  same  scale.     While  the  ordinary  photographic  lens  will 
cover  an  area  of  only  about  two  degrees  square,  this  covers  from  five  to  six 
degrees  square,  and  with  a  very  much  diminished  time  of  exposure.     It  has 
been  sent  to  the  Harvard  subsidiary  observatory  at  Arequipa,  Peru,  where 
it  is  employed  in  the  photography  and  spectroscopy  of  the  southern  heavens. 

The  new  telescopes  at  Greenwich  and  the  Cape  of  Good  Hope  have  the 
same  aperture,  but  are  much  longer.  Both  have  visual  finders  18  inches 
in  diameter. 

The  enormous  instrument  at  Meudon  (near  Paris)  has  also  two  tele- 
scopes combined,  —  a  visual  telescope  of  32  inches  aperture  and  a  photo- 
graphic of  25  inches,  each  55  feet  focal  length. 

Still  more  recently  the  Potsdam  Astrophysical  Observatory  has  mounted 
an  immense  instrument,  shown  in  the  frontispiece,  the  photographic  object- 
glass  of  which  has  a  diameter  of  31  £  inches,  with  a  focal  length  of  43  feet, 
and  the  visual  object-glass  a  diameter  of  20  inches.    This  long-focus  instru-  . 
ment  will,  however,  be  used  mainly  for  other  purposes  than  charting. 


STAR  MOTIONS 

537.   In  contradistinction  from  the  planets,  or  "wanderers," 
the  stars  are  called  "fixed,"  because  they  keep  their  relative  Theso- 
positions  and  configurations  sensibly  unchanged  for  centuries.  called  fixed 
Delicate  observations,  however,  separated  by  sufficient  intervals  moving, 
of   time,   show  that  the   fixity  is   not  absolute.      Nearly  two 
hundred  years  ago  (in  1718)  it  was  discovered  by  Halley  that 
Arcturus  and  Sirius  had  changed  their  places  since  the  days  of 
Ptolemy,  having  moved  southward,  the  first  by  a  full  degree 
and  the  other  about  half  as  much.     Indeed,  even  to  the  naked 
eye,  these  two  stars  no  longer  fit  certain  alignments  described 
by  Ptolemy. 


486 


MANUAL   OF   ASTRONOMY 


Common 
motions  due 
to  earth's 
motions 
only  ap- 
parent. 


Proper 
motions 
determined 
by  com- 
parison of 
old  with 
recent  star- 
catalogues. 


Modern  observations  show  clearly  that  the  stars  are  really  all 
in  motion,  "drifting"  upon  the  celestial  sphere.  Not  only  so, 
but  the  spectroscope  now  makes  it  possible  to  measure  their  rate 
of  motion  towards  or  from  the  earth,  and  it  appears  on  the 
whole  that  their  velocities  are  of  the  same  order  as  those  of 
the  planets  :  they  are  flying  through  space  incomparably  more 
swiftly  than  cannon-shot,  and  it  is  only  because  of  their  incon- 
ceivable distance  from  us  that  they  seem  to  go  so  slowly. 

538.  Common  Motions.  —  If  we  compare  a  star's  position  (i.e., 
its  right  ascension  and  declination)  as  determined  to-day  by  a 
meridian-circle  with  that  observed  one  hundred  years  ago,  it  will 
always  be  found  to  have  altered  considerably.     The  change,  how- 
ever, is  mainly  due,  not  to  any  real  change  in  the  position  of  the 
star,  but  to  precession,  nutation,  and  aberration,  already  dis- 
cussed (Sees.  165-171). 

These  depend  upon  variation  in  the  direction  of  the  earth's 
axis  and  upon  the  swiftness  of  her  orbital  motion  and  are  not 
real  changes  of  the  star's  direction  from  the  earth.  They  are 
only  apparent  displacements  and  are  called  "  common  "  motions 
because  they  are  shared  alike  by  all  stars  in  the  same  region  of 
the  sky.  They  do  not  in  the  least  affect  their  apparent  con- 
figurations and  angular  distances  from  each  other. 

539.  Proper    Motions.  —  But    after   allowing   for   all   these 
common  motions  of  the  stars,  it  generally  appears  that  in  the 
course  of  a  century  the  stars  have  really  changed  their  places 
with  reference  to   each   other,   each   having   a   motus  peculiaris, 
or  " proper  motion"  of  its  own,  the  word  "proper"  being  here 
the  antithesis   of  "  common."     Of  two  stars   side   by  side  in 
the  same  telescopic  field  of  view  the  proper  motions  may  be 
very  different  in  amount,  or  even  directly  opposite,  while  the 
common  motions,  due  to  precession,  etc.,  are,  of  course,  sensibly 
identical. 

About  175  stars  are  at  present  known  to  have  a  proper  motion 
exceeding  1"  annually,  but  the  number  is  being  constantly 


THE    STARS  487 

increased  by  additions  from  among  the  fainter  stars.  Even 
the  largest  of  these  proper  motions  (always  expressed  in  seconds 
of  arc)  is  very  small. 

The  maximum  at  present  known  (discovered  in  1898)  is  that  of  a  little   Maximum 
star  of  the  eighth  magnitude,  known  as  "  G.C.Z.,  V,  No.  243  "  (i.e.,  Gould's   known  8".7 
Cordova  Zones,  Fifth  Hour,  No.  243),  which  drifts  8".7  yearly.     The  next  yearlv- 
in  magnitude,  and  for  a  long  time  at  the  head  of  the  list,  is  that  of  the 
seventh-magnitude  star,  1830  Groombridge,  the  so-called  "runaway  star,"  . 
which  has  an  annual  drift  of  7".     Neither  of  these  stars  is  visible  to  the 
naked  eye.     It  will  take  two  hundred  years  for  the  first  of  them  to  drift  a 
distance  equal  to  the  moon's  apparent  diameter. 

As  might  be  expected,  the  proper  motions  of  the  bright  stars  Average 
average  higher  than  those  of  the  faint  ones,  since,  on  the  whole.  motlon 

.       °  greater  for 

the  bright  stars  are  nearer ;   but  the  faint  stars  are  so  much  the  nearer 
more  numerous  that  among  them  many  drift  faster  than  any  of  stars- 
the  fewer  bright  ones. 

The  average  proper  motion  of  the  first-magnitude  stars  is 
about  i/;  annually,  and  that  of  the  sixth-magnitude  stars  (the 
smallest  visible  to  the  naked  eye)  is  about  ^  of  a  second. 

These  motions  are  always  sensibly  rectilinear. 

Table  IV  of  the  Appendix,  in  connection  with  other  matters,  gives  the 
proper  motions  of  about  forty  of  the  nearer  stars  which  also,  as  a  rule,  are 
the  stars  having  the  larger  proper  motions. 

Hitherto  the   determination    of   proper   motions    has  rested  Advantage 
almost  entirely  upon  the  comparison  of  remotely  dated  star-  ofPh°t°g- 
catalogues,   but  it  is  likely  that  hereafter  much  more  rapid  determining 
progress  will  be  made  by  the  comparison  of  photographic  charts,  Pr°Per 
in  which  consideration  of  the  common  motions   is  unnecessary, 
as  these  affect  alike  all  the  stars  on  each  negative. 

540.   Real  Motions  of  Stars.  —  The  proper  motion  of  a  star  Real  motion 
gives  us  very  little  knowledge  as  to  the  star's  real  motion  in  ofastar- 
miles  unless  we  know  the  star's  distance,  nor  even  then  unless 
we  also  know  its  rate  of   motion  towards   or  from  us.     The 


488 


MANUAL   OF   ASTRONOMY 


Reduction 
of  proper 
motion  to 
miles  re- 
quires 
knowledge 
of  distance 


Formula 
for  cross 
motion. 


proper  motion  derived  from  the  comparison  of  the  catalogues  of 
different  dates  is  only  the  angular  value  of  that  part  of  the  whole 
motion  which  is  perpendicular  to  the  line  of  vision,  the  "cross" 
or  "  thwartwise  "  motion,  as  it  may  be  called.  A  star  moving 
directly  towards  or  from  the  earth  has  no  proper  motion, 

i.e.,  no  change  of  apparent  place 
to  be  detected  by  comparing 
observations  of  its  position. 

Fig.  174  illustrates  the  mat- 
ter.    If  a  star  really  moves  in  a 


To  the  Earth 


FIG.  174.  —  Components  of  a  Star's 
Proper  Motion 


year  from  A  to  B,  it  will  seem 
to  an  observer  at  the  earth  to 
have  traversed  the  line  Ah,  and  the  proper  motion  (in  seconds 

Ab 

of  arc)  will  be  206265  x  T. Since  Ab  cannot  possibly 

distance 

be  greater  than  AB,  we  are  able  in  some  cases  to  fix  a  minor 
limit  to  the  star's  velocity. 

According  to  the  determination  of  Briinnow,  accepted  until  lately,  the 
distance  of  1830  Groombridge  is  a  little  over  two  million  astronomical 
units;  and  therefore,  since  Ab  subtends  an  angle  of  1"  at  the  earth,  its 


length  must  be  at  least 


7x2  000000 


astronomical  units,  which,  reduced 


206265 

to  miles  and  divided  by  the  number  of  seconds  in  a  year,  corresponds  to  a 
velocity  exceeding  200  miles  a  second. 

More  recent  observations  by  Kapteyn  make  the  distance  of  this  star  con- 
siderably less  —  about  1  400000  astronomical  units  —  and  proportionally 
reduce  the  cross  motion,  Ab,  to  about  140  miles  a  second. 

For  the  star  of  greatest  proper  motion,  G.C.Z.,  V,  243,  the  cross  motion 
comes  out  about  80  miles  per  second,  so  that  the  "runaway  star"  still 
holds  the  record  for  real  swiftness. 

The  formula  for  this  "cross  "  or  "thwartwise  "  motion  (Ab  in  Fig.  174)  is 

©  (miles  per  second)  =  2.944  -  =  0.903  y  X  /A, 

where  /A  is  the  annual  proper  motion  of  the  star,  p  its  parallax  (both  in 
seconds  of  arc),  and  y  its  distance  in  "light-years."  (See  Sees.  546 
and  547.) 


THE   STARS  489 

In  many  cases  a  number  of  stars  in  the  same  region  of  the 
sky  have  proper  motions  practically  identical,  making  it  almost 
certain  that  they  are  in  some  sense  neighbors  and  really  con- 
nected, —  very  likely  by  community  of  origin.    In  fact,  it  seems  Gregarious 
the  rule  rather  than  the  exception  that  stars  which  are  appar-  tendency°f 
ently  near  each  other  and  about  alike  in  brightness  are  really 
comrades.     They  show,  as  Miss  Clerke  expresses  it,  a  distinctly 
"  gregarious  "  tendency.     In  certain  cases,  however,  there  are 
groups  of  stars  in  which  some  conspicuous  members  have  dif- 
ferent proper  motions  from   the   others,  and  these  discordant 
motions  will  in  time  destroy  the  configuration.     The  "  Dipper  " 
of  Ursa  Major  is  a  case  in  point.     The  two  extreme  stars,  a  Proper 
and  77,  are,  according  to  Flammarion,  moving  in  a  nearly  oppo-  motlons  in 
site    direction    from  the    others,    so  that   about  one   hundred 
thousand  years  ago  the  "  Dipper  "  was  no  dipper  at  all,  and  will 
not  be  one  a  hundred  thousand  years  hence.     The  other  stars  of 
the  group  maintain  their  configuration. 

541.    Motion  in  the  Line  of  Sight,  or  «  Radial  Velocity."1 —  spectro- 
Observations  of  the  proper  motions  of  stars  furnish  no  infor-  sc°Pic  deter- 

,,  i  •   i      ^i  T  mination  of 

mation  as    to    the    rate    at   which   the   stars    are   receding  or  ra<jiai 
approaching  ;  but  if  a  star  is  bright  enough  to  give  an  observ-  velocity. 
able  spectrum,  its  radial  velocity  can  be  determined  by  means 
of  the  spectroscope  and  the  application  of  the  Doppler-Fizeau  Application 
principle  (Sec.  254).     If  the  star  is  receding,  the  lines  of  its  °fthe, 
spectrum  will  be  shifted  towards  the  red,  and  towards  the  blue  Fizeau 
if  it  is  coming  nearer.     The  shift  is  ascertained  by  arranging  the  PrinciPle- 
telespectroscope  (Sec.  244)  so  that  by  a  comparison  prism  the 
observer  shall  have,  close  together  or  superposed,  the  spectrum  of 
the  star  he  is  dealing  with  and  of  some  substance  (hydrogen, 
sodium,  iron,  or  titanium)  whose  lines  are  present  as  dark  lines  in 

1  We  shall  follow  the  French  usage  in  employing  the  term  "  radial  velocity  " 
(vitesse  radiate)  to  denote  the  rate  at  which  a  body  is  changing  its  distance  from 
the  observer.  The  equivalent  expression,  "motion  in  line  of  sight,"  is  rather 
clumsy. 


490  MANUAL   OF   ASTRONOMY 

the  star  spectrum  ;  he  can  then  appreciate  and  measure  any  dis- 
placement of  the  stellar  lines,  as  illustrated  by  Fig.  98,  Sec.  254. 
First  success       Sir  William  Huggins,  in  1867,  was  the  first  to  apply  this 
bJ !8(37gginS    me^10^»  and  obtained  some  very  interesting  results  (especially 
the  determination  of  the  radial  motion  of  Sirius),  quite  sufficient 
to  establish  the  feasibility  of  his  method.     From  the  insufficient 
power  of  his  instruments,  however,  they  can  now  be  regarded 
only  as  approximations. 

The  work  was  followed  up  for  several  years  at  Greenwich 
Visual  and  some  other  places,  but  so  long  as  visual  observations  were 

observations  ,  .  ^  depended  upon 

unsatisfac-  /  X  1 

tory.  /  \        the  results   were 

not  very  satisfac- 
tory. Visual  ob- 
servations of  this 
kind  are  e  x- 
tremely  difficult; 
the  star  spectra 
are  very  faint,  the 
displacements  of 
the  lines  very 

FIG.  175.  —  Spectrum  of  a  Aurigse  compared  with  Hydrogen  minute,     and    the 

Vogel  lines    themselves 

often  broad  and  hazy  and  ill  adapted  for  accurate  measurement. 

In  the  case  of  the  nebulae,  however,  which  give  spectra  con- 

Keeier's        taining  sharp,  bright  lines,  Professor  Keeler  of  the  Lick  Observa- 

nebui^13         ^Ory  ^as  ma(^e  visual  observations  which  fairly  compete  with 

photographic  work. 

542.    Spectrographic  Determination  of  Radial  Velocity.  —  The 

unsatisfactory  results  of  visual  observations  led  Vogel  in  1888- 

Application    89  to  apply  photography,  and  with  immediate  success.     In  this 

rapVy  °        case  ^e  difficulties  arising  from  the  faintness  of  the  star  spectra 

Vogei's         can  be  largely  overcome  by  prolonged  exposure,  and  all  necessary 

measurements  can  be  made  at  leisure  under  the  microscope. 


THE   STARS  491 

Fig.  175  (borrowed  by  permission  from  Frost's  translation  of  Scheiner's 
Astronomical  Spectroscopy)  shows  very  perfectly  the  actual  appearance  of 
part  of  the  negative  of  the  spectrum  of  a  Aurigae  (Capella)  and  the  corre- 
sponding part  of  the  solar  spectrum  as  seen  under  the  microscope  with 
which  the  measurements  are  made.  The  solar  spectrum  is,  of  course,  on 
a  separate  plate,  but  this  plate  and  the  star  negative  are  clamped  together 
so  as  to  make  the  lines  correspond  and  facilitate  the  identification  of  lines 
in  the  star  spectrum.  (Note  in  passing  the  perfect  correspondence  between 
the  spectrum  of  this  star  and  that  of  the  sun.)  The  sharp  black  line 
which  crosses  the  narrow  star  spectrum  is  the  "  Hydrogen  y  "  bright  line 
in  the  spectrum  of  a  Geissler  tube  placed  in  the  cone  of  rays  about  2  feet 
above  the  slit-plate  and  illuminated  by  electricity  for  a  few  seconds  at 
different  times  during  the  long  exposure  (an  hour  or  so)  which  is  required 
for  the  star  spectrum. 

One  sees  easily  that  in  this  case  the  star  line  is  shifted  slightly  to  the 
right,  but  it  appears  to  be  so  poorly  defined  that  accurate  measurement 
would  be  difficult.  For  the  methods  by  which  this  difficulty  is  overcome,  and 
for  the  corrections  required  on  account  of  the  motion  of  the  earth1  and  other 
causes,  the  reader  is  referred  to  the  book  from  which  the  figure  is  taken. 

Fig.  176  is  from  a  photograph  of  the  new  Potsdam  spectrograph, 
attached  to  the  great  telescope  shown  in  the  frontispiece.  It  is  a  much 
more  powerful  and  perfect  instrument  than  that  used  by  Vogel  in  the 
work  above  mentioned. 

Rejcent  investigations  show  a  curious  relation  between  the  velocity  and 
the  spectral  type  of  stars,  which  would  seem  to  indicate  that  the  motion  of 
a  star  is  gradually  accelerated  while  the  spectrum  changes  from  the  earlier 
to  later  types. 

Table  V  of  the  Appendix  presents  the  results  of  Vogel  for  the  fifty-one 
stars  that  he  had  been  able  to  deal  with  up  to  1892,  with  the  addition  of 
one  or  two  from  other  observers.  His  telescope  had  an  aperture  of  only 
11  inches,  which  limited  him  to  the  brighter  stars.  It  has  now  been 
replaced  by  the  much  larger  instrument  shown  in  the  frontispiece. 

The    maximum    velocity    indicated    by   his    observations   of  Maximum 
1888-89   is  that  of  a  Tauri,   30.1   miles  a  second,   receding.  radiai 
The  next  in  order  is  that  of  7  Leonis,  24.1  miles,  approaching.  velocity 

so  far 

Belopolsky,  at  Pulkowa,  has   since  found  for  £  Hercules  the  measured 
higher  velocity  of  44  miles,  approaching  ;  and  Campbell,  at  the  about  6° 

miles  a 

1  Spectrographic  measures  are  now  precise  enough  to  give  a  fair  approxima-  s<     n  ' 
tion  to  the  earth's  orbital  velocity  and  the  distance  of  the  sun. 


492 


MANUAL   OF   ASTRONOMY 


Lick  Observatory,  finds  for  ft  Cassiopeia  the  still  higher  velocity 
of  61  miles,  also  approaching,  and  for  8  Leporis  and  6  Canis 
Majoris  a  nearly  equal  receding  velocity. 

Since  1890  the  same  line  of  work  has  been  taken  up  success- 
fully by  many  observers,  especially  by  Belopolsky  at  Pulkowa, 


FIG.  176.  — The  New  Potsdam  Spectrograph 

and  in  this  country  by  Keeler  and  Campbell  at  the  Lick 
Observatory,  and  by  Frost  at  the  Yerkes.1  Fig.  177  is  enlarged 
from  one  of  Frost's  photographs  of  the  spectrum  of  Arcturus 
(a  positive  in  this  case)  compared  with  that  of  the  metal  titanium, 

1  See  Fig.  180,  on  page  505,  for  the  Yerkes  spectrograph. 


THE  STARS 


493 


which  has  been  found  specially  advantageous  for  such  compari- 
sons. The  lack  of  perfect  coincidence  of  the  titanium  lines  of 
the  star  with  those  of  the  metal  indicates  that  the  earth  and 
star  were  approaching  at  a  speed  of  eleven  miles  a  second. 
This  relative  velocity  is  partly  due  to  the  "  line  of  sight "  com- 
ponent of  the  earth's  orbital  motion,  the  radial  velocity  of  the 
star  being  only  about  three  miles  a  second. 

The  star  spectrum  is  of  the  solar  type  (Sec.  568). 


Metal 


Star 


Metal 


4400  4500 

FIG.  177.  —  Spectrum  of  Arcturus  compared  with  Titanium 
Frost 

Observations  by  Humphreys    and    Mohler  of  Baltimore    in  Causes 
1895   (already  mentioned  in  Sec.  256)  show  that  under  heavy  ^^ 
pressure  the  spectrum  lines   of  many  elements  shift  slightly  results  for 
towards  the  red,  very  much  as   if  the  luminous  object  were  radial 

motion. 

receding.  The  shift  under  a  given  pressure  is,  however,  dif- 
ferent for  different  substances  and  for  different  lines  of  the 
same  substance.  It  is  always  minute,  never,  even  under  a 
pressure  of  ten  or  twelve  atmospheres,  exceeding  the  displace- 
ment that  would  be  due  to  a  receding  velocity  of  1  or  2  miles  a 
second,  but  it  is  quite  sufficient  to  require  to  be  examined  and 
taken  into  account  in  all  applications  of  Doppler's  principle. 

543.  The  Sun's  Way,  or  Motion  of  the  Solar  System.  —  The  The  sun's 
sun,  like  other  "  stars,"  is  traveling  through  space,  taking  with  motion  ** 
it  the  earth  and  the  planets. 


494 


MANUAL   OF   ASTRONOMY 


Determina- 
tion of  its 
direction  by 
means  of 
proper 
motions  of 
stars. 


Determina- 
tion by 
radial 
motions. 


Apex  of  the 
sun's  way : 
approxi- 
mate posi- 
tion. 


Sir  William  Herschel  was  the  first  to  investigate  and  deter- 
mine the  direction  of  this  motion,  more  than  a  century  ago. 
The  principle  involved  is  this :  the  apparent  motion  of  a  star 
relative  to  the  sun  is  made  up  of  its  own  real  motion  combined 
with  the  sun's  motion  reversed.  If  the  stars,  therefore,  were 
absolutely  at  rest,  they  would  apparently  all  drift  bodily  in  a 
direction  opposite  to  the  sun's  real  motion.  If,  as  is  the  fact, 
they  themselves  are  in  motion,  and  if  their  motions  are  indis- 
criminately in  all  possible  directions  (an  assumption  probable  as 
an  approximation  to  the  truth,  but  which  can  hardly  be  proved 
as  yet),  there  will  be,  on  the  whole,  a  similar  drift.  Those  in 
that  quarter  of  the  sky  towards  which  we  are  approaching  will, 
on  the  whole,  open  out  from  each  other,  and  those  in  the  rear 
will  close  up  behind  us,  while  in  the  region  of  the  sky  between, 
they  will,  on  the  whole,  drift  backwards,  —  just  as  one  walking 
in  a  park  filled  with  people  moving  indiscriminately  in  different 
directions  would,  on  the  whole,  find  that  those  in  front  of  him 
appear  to  grow  larger,1  and  the  spaces  between  them  to  open 
out,  while  at  the  sides  they  would  drift  backwards,  and  in  the 
rear  close  up. 

Again,  from  the  radial  motions  of  the  stars  spectroscopically 
measured  a  result  can  be  obtained.  In  the  portion  of  the 
heavens  towards  which  the  sun  is  moving  the  stars  will,  on  the 
whole,  seem  to  approach,  and  in  the  opposite  quarter  to  recede. 

The  individual  motions,  proper  and  radial,  lie  in  all  direc- 
tions ;  but  when  we  deal  with  them  by  the  thousand  the  indi- 
vidual is  lost  in  the  general,  and  the  prevailing  drift  appears. 

About  twenty  different  determinations  of  the  point  in  the 
sky  towards  which  the  sun's  motion  is  directed  have  been  thus 
far  made  by  various  astronomers.  There  is  a  reasonable  accord- 
ance of  results,  and  they  all  show  that  the  sun,  with  its 

1  Theoretically,  of  course,  the  stars  towards  which  we  are  moving  must 
appear  to  grow  brighter  as  well  as  to  drift  apart,  but  this  change  of  brightness, 
though  real,  is  entirely  imperceptible  within  a  human  lifetime. 


THE   STARS  495 

attendant  planets,  is  moving  towards  a  point  on  the  borders  of  the 
constellation  of  Hercules,  having,  according  to  Newcomb,  a  right 
ascension  of  about  277°. 5,  and  a  declination  of  about  35°.  This 
point  is  called  the  Apex  of  the  sun's  way.^ 

There  is,  however,  a  curious  systematic  difference  between  Uncertainty 
the  results  obtained  by  comparing  the  proper  motions  of  stars  as  to  exact 
that  drift  very  slightly  with  those   that  drift  more  rapidly. 
Dividing  them  into  four  groups,  some  550  of  the  slower  stars 
give  for  the  "  apex  "  a  declination  of  about  42°,  those  of  the 
next  grade  of  about  40°,  those  still  nearer  about  35°,  while 
those  that  are  nearest  us,  or  at  least  have  the  largest  proper 
motion,  push  the  point  still  nearer  to  the  equator,  to  a  declina- 
tion of  about  30°.     The  right  ascension  deduced  for  the  apex 
shows  no  such  systematic  discordance. 

This  probably  indicates  that  the  motions  of  the  stars  are  not 
absolutely  indiscriminate,  but  that  those  that  are  near  to  us 
have  some  common  drift  of  their  own.1 

As  to  the  velocity  of  the  sun's  motion  in  space,  the  spectro-  Velocity 
scopic  results,  which  are  on  the  whole  more  trustworthy  since  a^ut 
they  involve  no  assumption  as  to  the  distance  of  the  stars,  indi-  second, 
cate  that  it  is  about  11  miles  a  second,  which  probably  is  very 
near  the  truth. 

544.   The  Imagined  "  Central  Sun. "  —  We  mention  this  sub-  NO  central 
ject  simply  to  say  that  there  is  no  satisfactory  foundation  for  s 
the  belief  in  the  existence  of  such  a  body.     The  idea  that  the 
motion  of  our  sun  and  of  the  other  stars  is  a  revolution  around 
some  great  central  sun  is  a  very  fascinating  one  to  certain  minds, 
and  one  that  has  been  frequently  suggested.     It  was  seriously 
advocated  half  a  century  ago  by  Maedler,  who  placed  this  center 
of  the  universe  at  Alcyone,  the  principal  star  in  the  Pleiades. 

It  is  certainly  within  bounds  to  deny  that  there  is  any  con- 
clusive evidence  of  such  a  motion,  and  it  is  still  less  probable 
that  the  star  Alcyone  is  its  center,  if  the  motion  exists.  (But 
see  Sec.  609,  last  paragraph.) 

1  See  Addendum  D,  at  beginning  of  book. 


496 


MANUAL   OF   ASTRONOMY 


So  far  as  we  can  judge  at  present,  it  is  most  likely  that  the  stars  are 
moving,  not  in  regular  closed  orbits  around  any  center  whatever,  but 
rather  as  bees  do  in  a  swarm,  —  each  for  itself,  under  the  action  of  the 
predominant  attraction  of  its  nearest  neighbors.  The  solar  system  is  an 
absolute  monarchy,  with  the  sun  supreme.  The  great  stellar  system  appears 
to  be  a  republic,  without  any  such  central  and  dominant  authority. 


PARALLAX   AND   DISTANCE   OF   THE   STARS 

545,  Heliocentric  or  Annual  Parallax.  —  This  has  already 
been  defined  (Sec.  78)  as  the  difference  between  the  direction 
of  a  star  seen  from  the  sun  and  from  the  earth,  which  difference, 
if  the  star  is  not  at  the  pole  of  the  ecliptic,  varies  through- 
out the  year  with  an  annual  periodicity.  In  the  case  of  a  star 
the  geocentric  or  "diurnal"  parallax  is  absolutely  insensible, 
—  hopelessly  beyond  all  present  power  of  measurement. 

When,  therefore,  we  speak  of  a  stars  parallax  the  heliocen- 
tric parallax  is  to  be  understood.  Moreover,  unless  otherwise 
clearly  indicated,  the  maximum  value  of  the  star's  heliocentric 
parallax  is  always  meant.  Twice  a  year  the  earth  is  so  situated 
that  the  sun  and  star  are  90°  apart  in  the  sky,  when  the  longi- 
tude (celestial)  of  the  sun  is  90°  greater  or  less  than  that  of  the 
star.  At  that  moment  the  radius  vector  of  the  earth's  orbit  is 
perpendicular  to  a  line  drawn  from  the  earth  to  the  star,  and 
the  star's  annual  parallax  has  its  greatest  possible  value. 

The  parallax  of  a  star  may  therefore  be  defined,  as  the  term 
is  ordinarily  used,  to  be  the  angle  subtended  by  the  semi-major 
axis  of  the  earth's  orbit  when  viewed  perpendicularly  from  the 
star.  In  Fig.  178,  R  is  the  distance  from  the  earth  to  the  sun, 
D  from  the  sun  to  the  star,  and  the  angle  p  is  the  star's  paral- 
lax. If  we  can  measure  prr  (i.e.,  p  in  seconds  of  arc),  the  dis- 
tance of  the  star  at  once  follows  from  the  equation 

D-      R       -R      206265 

sin  p"  ~  p"     '• 

R  being  the  radius  of  the  earth's  orbit,  93  000000  miles. 


THE   STARS  497 

546.  The  Star's  Parallactic  Orbit. — We  may  look  at  the  Paraiiactic 
matter  differently.  In  accordance  with  the  principle  of  relative  c 
motion  (Sec.  354),  every  star  really  at  rest  (leaving  aberration 
out  of  the  account  at  present)  must  appear  to  us  to  move  in 
a  little  " parallactic  orbit"  186  000000  miles  in  diameter,  the 
precise  counterpart  of  the  earth's  orbit,  and  having  its  plane 
parallel  to  the  ecliptic  ;  in  this  little  orbit  the  star  keeps  always 
opposite  to  the  earth.  If  the  star  is  at  the  pole  of  the  ecliptic, 
we  see  this  parallactic  orbit  as  a  circle ;  if  in  the  ecliptic,  edge- 
wise, as  a  short  straight  line ;  in  intermediate  (celestial)  lati- 
tudes, as  an  oval.  The  semi-major  axis  of  this  apparent  paral- 
lactic orbit  is,  of  course,  the  star's  parallax.  (In  Fig.  178  the 


FIG.  178.  —  Heliocentric  Parallax 

dotted  oval  is  the  parallactic  orbit  of  the  star  s,  as  seen  from 
the  solar  system.)  If  the  star  is  drifting  (proper  motion),  this 
motion  will,  of  course,  be  combined  with  the  parallactic  move- 
ment, but  the  two  can  easily  be  separated  by  calculation. 

For  a  Centauri,  which  is  our  nearest  neighbor  among  the  Maximum 
stars  so  far  as  we  know  at  present,  the  parallax  is  only  0".75,  I 
and  there  are  but  seven  other  stars  which  are  known  to  have  a  known, 
parallax  as  large  as  0".3.     Indeed,  the  whole  number  of  those  0//-75for 
which  are  fairly  determined  to  have  a  parallax  of  0".l  and  over 
is  less  than  forty. 

547.   Unit  of  Stellar  Distance;  the  Light- Year.  —  The  distances  The  light- 
of  the  stars   are  so   enormous  that  the   radius  of  the   earth's  year' 
orbit,  the   astronomical  unit  hitherto   employed,   is  too  small 
for  a  convenient  measure.     It   is   better,   and  now  usual,  to 


498 


MANUAL   OF   ASTRONOMY 


Formula  for 
distance  in 
light-years. 


No  star  as 
near  as  three 
light-years. 


Difficulty  of 
measuring 
stellar 
parallax. 


Bessel's 
success  in 
1838. 


take  as  the  unit  of  stellar  distance  the  so-called  "light-year," 
i.e.,  the  distance  which  light  travels  in  a  year,  —  about  sixty- 
three  thousand l  times  the  distance  of  the  earth  from  the  sun. 

A  star  with  a  parallax  of  one  second  is  at  a  distance  of 
206265  astronomical  units.  Dividing  this  by  63000,  we  find 

3  26 

its  distance  in  light-years,  Dtl  =  — '-rr-  • 

p" 

A  star  with  a  parallax  of  half  a  second  is  at  a  distance  of 
6.52  light-years,  and  a  star  with  a  parallax  of  one  tenth  of  a 
second  is  at  a  distance  of  32.6  light-years. 

So  far  as  can  be  judged  from  the  scanty  data  available,  it 
appears  that  few,  if  any,  stars  are  within  a  distance  of  three 
light-years  from  the  solar  system,  —  not  one  has  thus  far  been 
discovered ;  that  the  naked-eye  stars  are  probably,  for  the  most 
part,  within  two  or  three  hundred  light-years;  and  that  many 
of  the  telescopic  stars  must  be  some  thousands  of  years  away. 

Table  IV  of  the  Appendix  contains  a  list  of  the  parallaxes 
thus  far  best  determined. 

548.  The  Determination  of  Stellar  Parallax.  —  It  is  obvious, 
therefore,  that  while  simple  enough  in  principle,  the  measure- 
ment of  a  star's  parallax  is  practically  one  of  the  most  delicate 
and  difficult  of  all  astronomical  operations  ;  and  there  is  no  way 
at  present  of  evading  the  difficulty  or  "  flanking  the  position," 
so  to  speak  (as  in  the  case  of  the  solar  parallax),  by  measuring 
the  parallax  of  some  near  object  or  utilizing  our  knowledge  of 
the  speed  of  light. 

Many  attempts  were  made  by  early  astronomers  to  measure 
the  parallax  of  stars,  but  with  no  real  success  until  Bessel,  in 
1838,  succeeded  in  determining  the  parallax  of  61  Cygni,  a 
little  star  of  the  sixth  magnitude,  which  had  for  some  time  been 

1  This  number  is  found  by  dividing  the  number  of  seconds  in  a  sidereal  year, 
31  558149,  by  499,  the  number  of  seconds  required  by  light  to  travel  from  the 
sun  to  the  earth.  The  exact  quotient  is  63243.  The  light-year  bears  to  the 
astronomical  unit  almost  exactly  the  same  ratio  as  the  mile  to  the  inch. 


THE   STARS  499 

interesting  astronomers  on  account  of  its  great  proper  motion 
of  5"  a  year.  He  made  his  observations  with  a  heliometer  and 
ascertained  its  parallax  to  be  about  half  a  second,  but  more 
recent  determinations  bring  it  down  to  0".40. 

Almost  simultaneously  Henderson  announced  the  parallax  of  Henderson 
a  Centauri  as  0".9,  according  to  meridian-circle  observations  and.£ 
at  the  Cape  of  Good   Hope.     The  star   has    a   large    proper 
motion  and  is  one  of  the  brightest  in  the  heavens,  but  is  not 
visible  in  our  latitudes.     It  still  holds  its  place  as  our  nearest 
neighbor,  though  later  observations  show  that  its  parallax  is 
only  0".75. 

Two  methods  of  procedure  have  thus  far  been  used,  known 
as  the  absolute  method  and  the  differential  method. 

549.  The  Absolute  Method.  —  This  consists  in  making  with  a  The  abso- 
meridian-circle,  or  some  equivalent  instrument,  numerous  obser- 
vations of  the  star's  apparent  right  ascension  and  declination 
throughout  the  year,  especially  at  the  two  seasons  when  the 
parallax  has  its  largest  value.  These  observations  are  then  care- 
fully corrected  for  aberration,  precession,  and  nutation,  also  for 
the  star's  proper  motion,  and  for  any  known  errors  due  to  the 
action  of  the  seasons  on  the  instrument.  If  the  observations 
and  their  corrections  are  perfectly  accurate,  they  will  give  a 
set  of  slightly  different  positions  for  the  star  during  the  year, 
which,  when  plotted,  will  all  fall  on  the  circumference  of  a  little 
oval,  —  the  star's  "  parallactic  orbit."  One  half  the  angular 
length  of  the  orbit  will  be  the  star's  parallax. 

But  the   corrections   to  be  applied  to  the  observations  are  Embar- 
enonnous  compared  with  the  parallax  itself.     While  the  paral-  rassed  by 

.  ,      _         ,  large  correc- 

lax  is  only  a  fraction  of  a  second,  the  aberration  corrections  run  tions. 
up  to  41".  The  instrumental  correction  is  especially  trouble- 
some, because  it  runs  its  course  yearly,  just  as  the  parallax  does, 
and  any  outstanding  error  confounds  itself  with  the  parallax  in 
a  manner  almost  inextricable.  Hence,  comparatively  little  suc- 
cess has  attended  operations  of  this  sort,  though  it  was  by  such 


500 


MANUAL   OF   ASTRONOMY 


The  differ- 
ential 
method. 


It  avoids 
large  cor- 
rections. 


observations  that  the  parallax  of  a  Centauri  was  first  detected, 
as  already  stated. 

550.  The  Differential  Method.  —  This  consists  in  determining 
the  position  of  the  suspected  star  at  different  times  during  the 
year,  not  absolutely,  but  with  reference  to  the  smaller  stars  appar- 
ently near  it,  though  presumably  at  a  great  distance  beyond.  This 
almost  entirely  obviates  the  difficulty  due  to  aberration,  preces- 
sion, and  nutation,  since  these  affect  all  the  stars  concerned  in 
the  operation  nearly  alike ;  the  observations  therefore  need  cor- 
rection only  for  the  difference  between  the  aberration,  etc.,  of 


FIG.  179. — Differential  Measurement  of  Parallax 

the  investigated  star  and  that  of  each  of  its  neighbors,  and  this 
small  differential  correction  can  be  easily  computed  with  very 
great  accuracy.  To  a  considerable  extent  also  the  method 
evades  the  effect  of  refraction  and  that  of  temperature  disturb- 
ances upon  the  instrument,  since  any  displacement  of  the  instru- 
ment does  not  perceptibly  affect  the  relative  position  of  the  stars 
seen  through  it.  Per  contra,  the  method  measures,  not  the  whole 
parallax  of  the  star  investigated,  but  only  the  difference  between 
its  parallax  and  that  of  the  stars  with  which  it  is  compared. 

Suppose,  for  instance  (Fig.  179),  that  in  the  same  telescopic 
field  of  view  we  have  the  star  s,  which  is  near  us,  the  stars 


THE    STARS  501 

x  and  y,  which  are  so  remote  that  they  have  no  sensible  parallax 
at  all,  and  the  star  2,  which  is  more  remote  than  s  but  has  a 
sensible  parallax  of  its  own.  s  and  z  will  describe  their  paral- 
lactic  orbits  every  year,  just  alike  in  form,  and  parallel,  but  the 
orbit  of  s  will  be  much  larger  than  z's.  If  now,  during  the 
year,  we  continually  measure  the  distance  and  the  direction  from 
x  or  y  to  the  apparent  places  of  s  and  z  in  their  parallactic  orbits,  Parallax 
the  results  will  give  us  the  true  dimensions  of  their  two  orbits.  nieasured 

is  only  the 

If,  however,  we  had  taken  z  as  the  reference  point  from  which  difference  of 
to  measure  the  parallactic  motion  of  s,  we  should  have  found  Parallax 
less  than  the  true  value,  as  is  obvious  from  the  figure.     Con-  stars> 
sidering  only  the  measures  made  at  the  moments  when  s  and  z 
are  at  the  extremities  of  their  parallactic  orbits,  the  lines  really 
measured  from  the  star  z  to  s  will  be  ea  and/6.     If  we  assume 
that  the  parallax  of  z  is  insensible,  i.e.,  that  its  parallactic  orbit 
is  a  mere  point,  these  measured  lines  must  be  used  in  computa 
tion  as  if  they  were  reckoned  from  the  point  z  and  were  zc  and 
zd ;  the  major  axis  of  the  parallactic  orbit  of  s  would  then  come 
out  as  cd  instead  of  ab,  and  the  computed  parallax  cs  will  be  less 
than  the  true  parallax  as  by  the  amount  ac,  which  equals  ez,  the 
parallax  of  z. 

It  follows  that  if  the  measurements  are  absolutely  accurate,  Parallax  too 
the  parallax  deduced  by  this  method  can  never  be  too  large,  small:  dis~ 

tance  too 

but  may  be  too  small,  —  the  distance  of  the  star  will  be  more  great. 
or  less  exaggerated.  If,  however,  the  small  reference  stars  are 
so  remote  that  their  parallax  and  proper  motions  are  really 
insensible  (i.e.,  less  than  0".01),  the  changes  in  the  relative  posi- 
tion of  the  star  under  investigation,  after  the  correction  for 
its  proper  motion  has  been  applied,  will  be  due  simply  to  its 
parallax. 

551.   Instrumental  Work.  —  If  the  comparison  stars  are  very  instrument: 
near    the    one    under    investigation,    the    necessary    measure-  filarmicrom- 
ments  may  be  made  with  the  filar  micrometer;  but  if  the  dis-  heiiometer. 
tance  exceeds  a  few  minutes,  we  must  resort  to  the  heiiometer 


502 


MANUAL   OF   ASTRONOMY 


Photog- 
raphy also 
used. 


Large  proper 
motion  the 
best  indica- 
tion of  prob- 
able  near- 
ness. 


(Sec.  72),  with  which  Bessel  first  succeeded,  or  we  may  employ 
photography,  which  the  late  Professor  Pritchard  at  Oxford  has 
done  with  some  success.  This  has  the  advantage  over  the 
heliometer  that  the  actual  observations  (in  taking  the  photo- 
graphs) can  be  made  much  more  rapidly  than  the  heliometer 
measures,  and  the  subsequent  measurement  of  the  photograph 
can  be  made  under  the  microscope  at  leisure;  moreover,  the 
suspected  star  can  be  compared  with  a  considerable  number  of 
others,  while  the  heliometer  is  usually  limited  to  two  or  three, 
on  account  of  the  long  time  required  to  make  each  complete 
measurement.  On  the  other  hand,  when  the  suspected  star  is 
much  brighter  than  the  reference  stars  its  photographic  image 
is  so  large  and  hazy  as  to  render  the  measures  of  its  position 
difficult  and  uncertain. 

On  the  whole,  the  differential  method,  notwithstanding  the 
fundamental  objection  which  has  been  mentioned,  is  at  present 
much  more  trustworthy  than  the  absolute. 

Negative  Parallax.  Now  and  then  it  happens  that  the  obser- 
vations appear  to  show  a  small  negative  parallax  for  the  star. 
This  may  indicate  simply  insufficient  accuracy  of  observation  or 
computation,  or,  if  the  observations  have  been  made  by  the 
differential  method,  it  may  mean  that  the  investigated  star  is 
really  beyond  the  comparison  stars  and  therefore  has  a  smaller 
parallax  than  they,  so  that  the  difference  between  its  parallax 
and  that  of  the  comparison  stars  comes  out  negative.  Of  course 
a  real  "  negative  parallax  "  is  impossible.  It  would  mean,  as 
some  one  has  said,  that  "  the  star  is  somewhere  on  the  other 
side  of  nowhere." 

552.  Selection  of  Stars  to  be  examined  for  Parallax.  —  It  is 
obviously  necessary  to  choose  for  observations  of  this  sort  stars 
that  are  presumably  near.  The  most  important  indication  of 
proximity  is  a  large  proper  motion.  It  is  easy  to  see  that  if  the 
observer  were  brought  nearer  to  a  star,  the  rapidity  of  its  appar- 
ent drift  across  the  sky  would  be  increased ;  and  accordingly  it 


THE   STARS  503 

is  practically  certain  that  the  stars  of  large  proper  motion  average 
nearer  than  those  for  which  the  motion  is  smaller,  though  the 
indication  is  not  to  be  depended  on  in  any  individual  case : 
if  a  star  happened  to  be  moving  directly  towards  or  from  us, 
its  proper  motion  would  be  zero,  however  near  it  might  be. 
Brightness  is,  of  course,  also  confirmatory,  but  nearly  all  the 
bright  stars  have  been  already  attacked.  Their  number  is  not 
very  great,  and  the  majority  of  them  turn  out  to  be  much  farther 
away  than  61  Cygni.  Among  the  millions  of  faint  stars  it  is 
quite  likely  that  some  few  individuals  at  least  will  be  found 
nearer  than  even  a  Centauri. 

553.  Possible  Spectroscopic  Method  of  the  Future.  —  It  will  Parallax 
appear  later  that  in  the  case  of  certain  binary  stars  (Sec.  587),  ^Tectrch 
which  have  the  plane  of  the  orbit  nearly  directed  to  the  sun,  scopicobser- 
the  spectroscope  will  enable  us  to  determine  the  actual  speed  vatlonsof 

,  .  _.  „   binary  stars. 

with  which  they  move  in  this  orbit  and  the  true  dimensions  of 
the  orbit  in  miles.  Combining  this  with  the  apparent  dimen- 
sions  of  their  orbits  in  seconds  of  are,  it  will  be  possible  to  com- 
pute their  distance  far  more  accurately  than  by  any  direct 
measure  of  their  parallax.1  But  it  will  be  many  years  yet  before 
the  necessary  measures  can  become  available  in  more  than  one 
or  two  instances,  since  the  orbital  periods  of  the  binaries  which 
have  an  apparent  orbit  of  measurable  size  are  mostly  long,  and 
only  few  orbits  lie  in  a  favorable  position. 

554,  General  Conclusions.  —  It  is  obvious  that  the  data  so  far  Data  too 
obtained  are  too  scanty  to  warrant  many  general  conclusions.  fcan^rfor 

J  Jo  broad  gener- 

We  have  not  a  sufficient  number  of  well-defined  parallaxes  to  alizations. 

furnish  a  safe  basis  for  averages,  —  say  forty  or  fifty  only,  —  and 

the  smaller  ones  among  them  are  subject  to  a  probable  error  of 

at  least  twenty-five  per  cent.     Consequently  all  calculations  as 

to  mass,  brightness,  etc.,  of  individual  stars  are  likely  to  differ 

widely  from  the  truth.     It  is,  however,  already  clear  that,  taken 

in  classes,  the  stars  of  large  proper  motion  average  the  nearest, 

1  Wright  in  1905  tested  this  method  upon  Alpha  Centauri  and  obtained  a 
result  in  almost  perfect  accordance  with  that  determined  by  the  older  methods. 


504 


MANUAL   OF   ASTRONOMY 


Caution  in 

applying 

average 

results  to 

individual 

stars. 


the  distance  being  roughly  inversely  proportional  to  the  apparent 
rapidity  of  their  drift ;  and,  further,  that  on  this  assumption  the 
majority  of  the  stars  must  be  at  a  distance  greater  than  fifty 
light-years,  and  the  remoter  stars  in  all  likelihood  many  times 
more  distant  still. 

Something  similar  appears  to  be  true  in  the  relation  between 
the  brightness  of  the  stars  and  their  distance. 

Kapteyn,  from  stellar  parallaxes  already  determined,  also 
finds  evidence  of  a  roughly  uniform  distribution  of  stars  in 
space,  leaving  the  Milky  Way  out  of  the  question. 

Another  interesting  fact  appears,  viz.,  that  the  stars  which 
show  a  spectrum  like  the  sun's  are  on  the  average  much  nearer 
than  the  so-called  "  Sirian  "  stars. 

But  the  student  must  be  warned  again  that  he  cannot  safely 
apply  to  individuals  the  results  of  such  general  averages.  Any 
small  star  is  not  at  all  unlikely  to  be  really  brighter  and  larger 
than  a  bright  star  near  it,  just  as  in  the  case  of  two  persons, 
one  a  youth  and  the  other  a  man  of  mature  age,  it  would  be 
unsafe  to  predict  from  the  mere  difference  of  age  which  would 
have  the  longer  life. 

EXERCISES 

1.  Assuming  the  parallax  of  61  Cygni  as  0".40,  and  that  it  is  approach- 
ing the  sun  at  the  rate  of  34.5  miles  a  second,  how  many  years  will  it 
be  before  its  brightness  is  increased  10  per  cent  by  the  diminution  of  its 
distance?  Ans.    2050  years. 

2.  Assuming  the  distance  of  61  Cygni  as  8.15  light-years,  and  that  its 
radial  and  "  thwartwise  "  velocities  are  34.5  and  38  miles  a  second,  respec- 
tively, find  how  near  the  star  will  come  to  the  sun  if  it  keeps  up  this  motion 
uniformly,  and  how  long  it  will  take  to  reach  this  point  of  nearest  approach. 

(  Nearest  approach,  6.03  light-years. 
1  Time,  19900  years. 

3.  Make  the  same  calculation  for  a  Aquilae,  assuming  its  parallax  as 
0".20,  its  proper  motion  as  0".65  annually,  and  the  rate  at  which  it  is 
approaching  as  24  miles  a  second. 


Ans. 


THE   STARS 


505 


4.  What  would  be  the  time  required  to  make  the  journey  to  Sirius 
(parallax  0".38)  at  the  rate  of  60  miles  a  second,  and  the  fare  at  1  cent  a 
mile? 

5.  Deduce  the  formulae  of  Sec.  540,  viz.: 

®  (miles  per  second)  =  2.944  -  =  0.903  y  x  LI, 

P 
using  the  data  of  Sees.  546-547. 


FIG.  180.  —  Bruce  Spectrograph  of  the  Yerkes  Observatory  (1902) 


CHAPTER   XIX 


The  six 
magnitudes 

of  naked- 

eye  stars. 


THE   LIGHT   OF  THE   STARS 

The  Light  of  the  Stars  —  Magnitudes  and  Brightness  —  Color  and  Heat  —  Spectra  — 

Variable  Stars 

555.   Star  Magnitudes  —  The  term  "magnitude,"  as  applied 
to  a  star,  refers  simply  to  its  brightness  and  has  nothing  to  do 
with  its  apparent  angular  diameter.     Hipparchus  and  Ptolemy 
arbitrarily  graded  the  visible  stars  into  six  magnitudes,  the  stars 
f  ^    gixth  bei      the  faintest  visible  to  the  eye,  while  the  first 

* 

magnitude  comprises  about  twenty  of  the  brightest.  There  is 
no  known  reason  why  six  classes  should  have  been  constituted 
rather  than  eight  or  ten,  unless  perhaps  the  physiological  one 
that  ordinary  eyes  do  not  easily  recognize  differences  of  bright- 
ness sufficiently  small  to  warrant  a  more  refined  subdivision. 

After  the  invention  of  the  telescope  the  same  system  was 
extended  to  the  fainter  stars,  but  without  any  general  agree- 
ment, so  that  the  magnitudes  assigned  by  different  observers 
to  telescopic  stars  in  the  early  part  of  the  century  differ  enor- 
mously. Sir  William  Herschel,  especially,  used  very  high  num- 
bers, his  twentieth  magnitude  being  about  the  same  as  the 
fourteenth  on  the  scale  now  generally  used,  which  nearly  corre- 
sponds with  that  which  was  adopted  by  Argelander  in  his  great 
Durchmusterung  (Sec.  533). 

Of  course  the  stars  classed  together  under  one  magnitude  are 
not  exactly  alike  in  brightness,  but  shade  from  the  bright  to  the 
fainter,  so  that  exactness  requires  the  use  of  fractional  magni- 
les'  tudes.  It  is  now  usual  to  employ  decimals  giving  the  bright- 
ness of  a  star  to  the  nearest  tenth  of  a  magnitude.  Thus,  a 
star  of  4.3  magnitude  is  a  shade  brighter  than  4.4,  and  so  on. 

506 


Fractional 


THE   LIGHT   OF   THE   STARS  507 

A  peculiar  notation  was  employed  by  Ptolemy  and  used  by  Argelander   Argelander's 
in  his   Uranometria1  Nova.     It  recognizes   thirds  of  a  magnitude  as  the   peculiar 
smallest   subdivision.     Thus,  2,   2,3,   3,2,  and  3  express  the  gradations  notation- 
between  second  and  third  magnitude,  2,3  being  applied  to  a  star  whose 
brightness  is  a  little  inferior  to  the  second,  and  3,2  to  one  a  little  brighter 
than  the  third.     Note  the  comma ;  3,2  (3  comma  2)  must  not  be  confounded 
with  3.2  (3  point  2):  the  first  means  2f  magnitude,  the  other  3T2o  mag- 
nitude. 

556.  Stars  Visible  to  the  Naked  Eye.  —  Heis  enumerates  the 
stars  clearly  visible  to  the  naked  eye  in  the  part  of  the  sky 
north  of  35°  south  declination,  as  follows : 

1st  magnitude    ...       14        4th  magnitude    .     .     .       313  Number  of 

2d  «  ...       48       5th          «  ...       854  visible  stars 

3d  «  ...     152        6th  «  ...     2010  of  the  differ- 

ent  magm- 
Total 3391  tudes. 

According  to  Newcomb,  the  number  of  stars  of  each  magni- 
tude is  such  that  united  they  would  give,  roughly  speaking, 
about  the  same  amount  of  light  as  that  received  from  the  aggre- 
gate of  those  of  the  next  brighter  magnitude.  But  the  relation 
is  very  far  from  exact  and  fails  entirely  for  the  magnitudes 
below  the  eleventh,  the  smaller  stars  being  much  less  numerous 
than  this  law  would  make  them. 

557.  Light-Ratio  and  Scale  of  Magnitude.  —  It  was  found  by 
Sir  John  Herschel  about  1830  that  an  average  star  of  the  first 
magnitude  is  just  about  one  hundred  times  as  bright  as  one  of  First-magni- 
the  sixth,  and  that  for  the  naked-eye  stars  a  corresponding  ratio  tude  star 

J  equals  one 

had  been  roughly  maintained  by  former  observers  through  the  hundred  of 
whole  scale  of  magnitudes,  the  stars  of  each  magnitude  being  sixth  magm- 
approximately  two  and  one-half  times  as  bright  as  those  of  the 
next  fainter. 

Still,  on  the  star-maps  of  Argelander,  Heis,  and  others 
long  accepted  as  standards  there  are  notable  deviations  from 
a  consistent  uniformity,  and  in  1850  Pogson  proposed  the 

1  The  term  "Uranometria"  has  come  to  mean  a  catalogue  of  naked-eye  stars, 
like  the  catalogues  of  Hipparchus?  Ptolemy,  and  Ulugh  Beigh. 


508 


MANUAL   OF   ASTRONOMY 


"Absolute  Scale"  of  star  magnitudes,  adopting  the  fifth  root  of  one 
hundred,  2.512  +,  as  the  uniform  "light-ratio,"  adjusting  the  first 
six  magnitudes  to  fit  as  nearly  as  possible  the  magnitudes  of 
Argelander's  Durchmusterung,  and  then  carrying  forward  the 
scale  among  the  telescopic  stars.  Until  about  1885  this  scale 
had  not  been  much  used;  but  it  has  been  adopted  in  the  new 
"  Uranometrias "  made  at  Cambridge,  U.S.,  and  Oxford,  and 
is  now  rapidly  supplanting  all  the  arbitrary  scales  of  former 
observers.  On  this  scale  Aldebaran  and  Altair  are  very  nearly 
typical  "first-magnitude"  stars,  and  the  two  "pointers"  and 
Polaris  are  practically  "second-magnitude"  stars. 

558.  Relative  Brightness  of  Different  Star  Magnitudes.  —  In 
this  scale  the  "light-ratio"  (i.e.,  the  ratio  between  the  light  of 
two  stars  standing  just  one  magnitude  apart  in  the  scale)  is 
exactly  VlOO,  or  the  number  whose  logarithm  is  0.4000,  i.e., 
2.512.  Its  reciprocal  is  the  number  whose  logarithm  is  9.6000, 
viz.,  0.3981. 

If  bm  is  the  brightness  of  a  star  of  the  mth  magnitude 
(expressed  either  in  candle-power  or  some  other  convenient 
unit),  and  if  bn  is  that  of  a  star  of  the  nth  magnitude,  the  rela- 
tion between  their  light  is  given  by  the  fundamental  equation 

log  bm  -  log  bn  =       (n  -  m),  or  log  \          =       (n  -  m).     (1) 


(2) 


From  this,  conversely, 

(n-m)  =  —  (log  bm  -  log  bn)  =  2.5  log 


The  first  gives  the  relation  between  the  brightness  of  two 
stars  having  a  known  difference  of  magnitude  (n  —  m) ;  the 
second  the  difference  of  magnitude  between  two  objects  having 
a  known  ratio  of  brightness. 

For  example,  a  certain  variable  star  rises  seven  magnitudes  between 
the  minimum  and  maximum ;  how  much  does  its  brightness  increase  ? 

b  4 

log  r^  =  log  of  increase  of  brightness  =  r-r  x  7  =  2.8000. 


THE   LIGHT   OF   THE   STARS  509 

Looking  in  the  table  of  logarithms,  we  find  631  corresponding  to  this 
logarithm,  2.8000  ;  i.e.,  the  star  increases  in  brightness  631  times.  (Four- 
place  logarithms  are  always  sufficient.) 

Again,  Nova  Persei  increased  in  brightness  25000  times  between  Feb- 
ruary 20  and  22,  1901 ;  how  many  magnitudes  did  it  rise?  From  equa- 
tion (2)  the  rise  in  magnitude 

(n  -  m)  =  -£-  log  25000  =  -£•  x  4.3979  =  11  magnitudes  (nearly). 

If  the  star  were  of  the  eleventh  magnitude  on  February  20,  it  was  of  the 
zero  magnitude  on  the  22d. 

It  is  an  infelicity  of  this  scale  that  the  numerical  magnitudes  Zero  magni- 
decrease  with  the  brightness  of  the  object,  so  that  a  star  which,  *gd*t*^ 
like  Arcturus,  is  one  magnitude  brighter  than  Aldebaran  or  magnitudes. 
Altair  is  of  the  zero  magnitude,  while  Capella  and  Vega  are 
of  magnitude   0.2.      In   the   case   of  the  two  brightest  stars, 
Sirius  and  Can  opus,  we  run  past  the  zero  into  negative  num- 
bers,  the   magnitude  of  Sirius  being  —  1.43.      That  of  Jupi- 
ter at  opposition  is  about  —  2,  i.e.,  three  magnitudes  brighter  The  sun's 
than  Aldebaran.     On  this  scale  the  sun  is  about  the  -  26.3  magnitude 

—  26.3. 

magnitude. 

559.   Telescopic   Power  required  to  show  Stars  of   a   Given 
Magnitude.  —  If  a  good  telescope  just  shows  stars  of  a  certain 
magnitude,  then,  since  the  light-gathering  power  of  a  telescope 
depends  on  the  area  of  its  object-glass  (which  varies  as  the  Telescopic 
square   of  its  diameter),  we  must  have   a  telescope  with  its  P°werin 

/ relation  to 

aperture  larger  in  the  ratio  of  V2.512  (or  1.59) :  1,  in  order  to  starmagni- 
show  stars  one  magnitude  smaller;  i.e.,  the  aperture  must  be  tude- 
increased  1.6  times  (nearly).     A  tenfold  increase  in  the  diameter 
of  an  object-glass  theoretically  carries  the  power  of  vision  just 
five  magnitudes  lower. 

Assuming  what  seems  to  be  very  nearly  true  for  normal  eyes  Telescopic 
and  good  telescopes,  that  the  minimum  visibile  for  a  1-inch  aper-  ^^^ 
ture  is  a  star  of  the  ninth  magnitude,  we  obtain  the  following  little  to  show 
table  of  apertures  required  to  show  stars  of  a  given  magnitude,  certain 
the  formula  being,      m  =  9  -f-  5  x  log  of  aperture  (in  inches). 


510 


MANUAL   OF   ASTRONOMY 


Star  magnitude      .     .     . 

7th 

8th 

9th 

10th 

llth 

12th 

Aperture,  inches    .     .     . 

0.40 

0.63 

1.00 

1.59 

2.51 

3.98 

Star  magnitude 

13th 

14th 

15th 

16th 

17th 

18th 

Aperture,  inches    .     .     . 

6.31 

10.00 

15.90 

25.10 

39.80 

63.10 

Measure- 
ments of 
magnitudes 
and  bright- 


But  large  telescopes,  on  account  of  the  increased  thickness 
in  their  lenses,  which  causes  considerable  absorption  of  light, 
never  quite  equal  their  theoretical  capacity  as  compared  with 
smaller  ones. 

The  Yerkes  telescope  (40  inches  aperture)  will  barely  show 
stars  of  the  seventeenth  magnitude,  not  quite  one  magnitude 
fainter  than  the  smallest  visible  with  the  26-inch  telescope  at 
Washington.  But  the  number  visible  in  the  larger  instrument 
is  probably  fully  doubled. 

560.  Measurement  of  Magnitudes  and  Brightness.  —  Until 
within  the  last  twenty-five  years  all  such  measures  (with  a  few 
exceptions)  were  mere  eye  estimates,  and  such,  when  made  by 
experienced  observers,  are  still  valuable  and  much  used  in 
observing  changes  of  brightness,  as  in  the  case  of  variable 
stars. 

At  present,  however,  the  brightness  and  magnitude  of  all  the 
principal  stars  have  been  determined  instrumentally  by  photom- 
eters of  some  kind.  Still,  even  with  visual  photometers,  the  eye 
of  the  observer  is  the  ultimate  arbiter. 

No  satisfactory  means  has  yet  been  found  for  a  purely  instrumental 
measurement  of  starlight,  although  certain  promising  experiments  have 
been  made  by  Professor  Minchin  in  attempting  to  determine  the  lumi- 
nosity of  stars  by  its  effect  in  changing  the  electrical  resistance  of  selenium, 
and  the  method  may  ultimately  develop  into  something  valuable. 

The  instruments  at  present  used  are  nearly  all  based  on  one 
of  two  different  principles : 

Extinction          (1)    The  Method  of  Extinction,  in  which  the  instrument,  by 
photometers.  vaiying  the  aperture  of  the  telescope  by  an  "  iris  diaphragm," 


THE  LIGHT  OF  THE  STARS  511 

or  by  sliding  a  wedge  of  dark  glass  before  the  eye,  causes  the 
star  to  grow  fainter  until  it  vanishes. 

A  graduation  on  the  slider  that  carries  the  wedge,  or  a  scale 
that  measures  the  area  of  the  opening  in  front  of  the  object- 
glass,  determines  the  star's  brightness  as  compared  with  that 
of  some  standard  star  which  has  been  observed  with  the  same 
apparatus ;  but  the  observations  are  very  trying  to  the  eyes. 

Pritchard's  Uranometria  Oxoniensis  was  made  by  observations  with  such 
a  wedge -photometer  in  1895. 

(2)   The  Method  of  Equalization.     The  second  class  of  instru-  Equalizing 
ments  consists  of  such  as  equalize  the  brightness  of  the  star  Photome- 
investigated  to  that  of  some  "  standard  star  "  brought  into  the 
same  field  of  view  by  reflection,  or,  more  commonly,  to  the  light 
of  an  "  artificial  star  "  of  constant  brightness. 

This  artificial  star  is  usually  a  pinhole  through  which  shines 
a  small  lamp  (usually  a  frosted  electric  lamp)  fed  by  a  storage 
battery.  Its  image  is  made  to  fall  into  the  field  of  view  close 
by  that  of  the  star  to  be  measured,  and  its  brightness  is  varied 
at  pleasure  by  sliding  a  wedge  in  front  of  the  pinhole,  or  by  a 
polarization  arrangement  consisting  of  a  pair  of  Nicol  prisms, 
which  is  better  but  more  expensive.  The  eye  judges  when 
the  two  stars,  the  artificial  star  and  the  other,  are  apparently 
equal. 

With  instruments  of  tlris  class  Pickering  of  Cambridge  made  his  Har- 
vard Photometry,  and  Miiller  and  Kempf  at  Potsdam,  somewhat  later,  con- 
structed their  still  more  elaborate  and  accurate  catalogue  of  the  brightness 
of  thirty-five  hundred  stars  above  magnitude  seven  and  one-half,  north  of 
the  equator. 

Photometric  observations  in  many  cases  require  large  and  Probable 
somewhat  uncertain  corrections,  especially  for  the  absorption  errorof 

f  ,  , .  ,y,  photometric 

of   light   by  the    atmosphere    at    different    altitudes,   and  the  measures, 
final  results  of  different  observers  naturally  fail  of  absolute 
accordance.     Still,  the  agreement  between  the  different  recent 


512 


MANUAL  OF  ASTRONOMY 


photometric  catalogues  is  remarkably  close,  —  generally  between 
one  or  two  tenths  of  a  magnitude,  though  with  occasional 
notable  exceptions. 

Differences  of  color  embarrass  photometric  measurements 
made  by  either  of  the  methods  described,  because  it  is  impos- 
sible to  make  a  red  star  look  identical  with  a  blue  one  by  any 
mere  increase  or  diminution  of  brightness,  and  because  different 
observers  differ  in  setting  the  index  of  an  extinction  photometer 
according  to  the  color  of  the  star.  An  increase  in  aperture 
makes  red  stars  appear  relatively  brighter. 

Stars  differ  considerably  in  color.  The  majority  are  of  a  very  pure 
white,  like  Sirius,  but  there  are  not  a  few  of  a  yellowish  hue,  like  Capella, 
or  reddish,  like  Arcturus  and  Antares,  and  there  are  others,  mostly  small 
stars,  which  are  as  red  as  garnets  and  rubies.  We  also  have,  associated 
with  larger  stars  in  double-star  systems,  numerous  small  stars  which  are 
strongly  green  or  blue ;  and  a  few  large  stars,  Vega  for  instance,  are  dis- 
tinctly of  a  bluish  tinge,  like  an  electric  arc. 

561.  Photographic    Photometry.  —  Magnitudes    may  also    be 
determined  from  comparisons  of  the  diameters  of  star  images 
found  upon  photographic  plates.   These  photographic  magnitudes 
will  not  always  agree  with  the  visual,  because  the  sensitiveness 
of  the  plate  to  various  rays  of  light  does  not  correspond  to  that  of 
the  eye.    This  difference  is  most  marked  in  the  case  of  red  stars, 
which  fail  to  impress  themselves  strongly  upon  the  plates,  and 
evidently  bears  a  definite  relation  to  the  spectral  type  of  the 
star.    Magnitudes  corresponding  to  the  visual  have,  however, 
been  obtained  by  the  use  of  a  "  visual  luminosity  filter "  and 
specially  sensitized  plates.    The  photographic  method  is  often 
highly  advantageous  in  determining  the  change  of  brightness  of 
a  star,  as,  for  instance,  in  the  case  of  Eros  (Sec.  428). 

562.  Starlight  compared  with  Sunlight.  —  Zbllner  and  others 
have  endeavored  to  determine  the  amount  of  light  received  by 
us  from  certain  stars,  as  compared  with  the  light  of  the  sun. 
The  measures  are  very  difficult   and  the  result  considerably 


THE   LIGHT   OF   THE   STARS  513 

uncertain,   but,  according   to    Zollner,   Sirius  gives    us    about 
as  much  light  as  the  sun  does,  and  Capella  and  Vega 

7000  000000 

about  40QOQ  QOOOOO '  According  to  tnis»  a  standard  first-magni- 
tude star,  like  Altair  or  Aldebaran,  gives  us  about  AAAAAA* 

oOOOO  000000 

and  it  would  take,  therefore,  about  eight  billions  (English),  i.e., 
about  eight  million  million,  stars  of  the  sixth  magnitude  to  do 
the  same.  But  the  various  determinations  for  Vega  range  all 

the  way  from  60000\om(>0  to  80000o00000- 

Assuming  what  is  roughly  but  by  no  means  strictly  true,  that  Arge-  Total 
lander's  magnitudes  agree  with  the  absolute  scale,  it  appears,  on  the  basis   amount  of 
of  Zollner's  measurements,  that  the  324000  stars  of  his  Durchmusterung,    starllSht- 
all  of  them  north  of  the  celestial  equator,  give  a  light  about  equivalent  to 
240  or  250  first-magnitude  stars. 

How  much  light  is  given  by  stars  smaller  than  the  nine  and  one-half 
magnitude  (which  was  his  limit)  is  not  certain.  It  must  greatly  exceed 
that  given  by  the  larger  stars,  because  the  total  light  given  by  the  stars  of 
each  magnitude  is  always  several  times  as  great  as  that  given  by  the  stars 
of  the  preceding  magnitude.  As  a  rough  guess,  we  may  perhaps  estimate 
that  the  total  starlight  of  both  the  northern  and  southern  hemispheres  is 
equivalent  to  ab'out  3000  stars  like  Vega,1  or  1500  at  any  one  time. 
According  to  this,  the  starlight  on  a  clear  night  is  about  ^  of  the  light 
of  the  full  moon,  or  about  TS'O'G'QO^  °f  sunlight.  But  this  estimate  is 
hardly  more  than  guesswork.  It  is  pretty  certain,  however,  that  more 
than  half  of  this  light  comes  from  stars  which  are  entirely  invisible  to 
the  naked  eye. 

563.   Heat  from  the  Stars.  —  Doubtless  the  stars  send  us  heat,  stellar  heat, 
and  very  likely  the  proportion  of  their  heat  to  solar  heat  is 

1  According  to  Newcomb,  in  an  important  paper  published  in  January,  1902, 
"  The  total  light  of  all  the  stars  is  about  equal  to  that  of  600  stars  of  magnitude 
zero,  with  a  probable  error  of  one  fourth  of  its  whole  amount.'1'1 

This  is  equivalent  to  about  750  Vegas  instead  of  3000.  The  discrepancy  is 
mainly  due  to  a  much  lower  estimate  of  the  light  from  stars  below  the  ninth 
magnitude.  Professor  Newcomb,  however,  thinks  the  true  result  likely  to  be 
larger  rather  than  smaller  than  the  one  he  has  given. 


514 


MANUAL   OF   ASTRONOMY 


about  the  same  as  that  of  starlight  to  sunlight.  Various 
attempts  have  been  made  to  measure  it,  but  the  amount  is  so 
small  that  until  very  recently  no  apparatus  has  been  found 
sufficiently  sensitive  even  to  detect  it. 

About  1870  Huggins  and  Stone  in  England  thought  that 
they  had  found  distinct  indications  of  stellar  heat  by  the 
thermopile,  but  later  work  showed  that  the  results  were  not 
reliable.  About  1890  Boys  with  his  radio-micrometer  attempted 
the  problem,  but  could  obtain  no  measures  nor  even  any  indica- 
tions  of  stellar  heat.  In  1898  and  1900  Professor  E.  F.  Nichols, 
Recent  sue-  working  at  the  Yerkes  Observatory  with  an  apparatus  twenty 

cess  m  its      Qr  thirty  times  as  sensitive  as  that  of  Boys,  succeeded  in  get- 
measure-  ^ 
ment.            ting  distinct  deflections  upon  his  scale  from  the  rays  of  Vega, 

Arcturus,  Jupiter,  and  Saturn,  indicating  heat  radiations  in  the 
ratio  of  1,  2.2,  4.7,  and  0.74,  respectively,  after  correction  for 
the  different  zenith-distances  of  the  objects.  That  is,  Arcturus 
appeared  to  give  2.2  times  as  much  heat  as  Vega,  Jupiter  4.7 
as  much,  and  Saturn  about  f . 

The  observations  indicate  also  that  Arcturus,  in  the  zenith,  sends  to  a 
square  foot  of  the  earth's  surface  as  much  heat  as  would,  come  to  it  from 
a  standard  candle  at  a  distance  5.8  miles,  provided  none  of  the  candle  heat 
were  absorbed  in  passing  through  the  air. 

Under  the  same  conditions  the  heat  from  Vega  equals  that  received 
from  a  candle  8.7  miles  distant. 

But  the  correction  for  the  absorption  of  the  candle  heat  is  so  uncertain 
that  these  last  results  are  subject  to  large  errors.  The  scale  deflection  in 
the  case  of  Arcturus  was  a  little  more  than  a  millimeter. 

564.  Total  Amount  of  Light  emitted  by  Certain  Stars.  —  When 
we  know  the  parallax  of  a  star  (and  therefore  its  distance  in 
astronomical  units  or  light-years)  it  is  easy  to  calculate  its  light 
emission  as  compared  with  that  of  the  sun.  If  I  be  the  light 
received  from  a  star  on  the  earth,  expressed  in  terms  of  sunlight, 
and  L  the  light  it  emits  as  compared  with  the  sun,  L  =  I  X  IP 
(astronomical  units),  or  (nearly)  4000  000000  ZD2  (lightly  ears). 


THE   LIGHT   OF   THE   STARS  515 

For  Sirius,  referring  to  Table  IV,  we  have  Dy  =  8.4  light- 

-,  7  1  T       4000  000000  ,X2 

years  and  I  =  700UWO(HM)-     Hence,  L  =  7000  ooooeo  x  (8.4)'  =  40 

(nearly). 

Similarly  for  other  stars:  using  the  magnitudes  of  the  Harvard  Pho- 
tometry with  distances  from  Table  IV,  we  get  for  Polaris  (p  =  0".07)$ 
L  =  68  ;  Vega  (p  =  0".16),  L  =  44;  a  Centauri  (p  =  0".75),  L  =  1.9; 
70  Ophiuchi  O  =  0".25),  £  =  0.41;  61  Cygni  (p  =  0".40),  Z=0.10; 
LI.,  21258  Q>  =  0".26),  Z  =  T^. 

565,   Why  the   Stars  differ  in  Brightness.  —  The   apparent  Three 
brightness  of  a  star,  as  seen  from  the  earth,  depends  both  on  causesof 

difference 

its  distance  and  on  the  quantity  of  light  it  emits,  and  the  latter  of  bright- 


depends  on  the  extent  and  the  luminosity  of  its  surface.  As  a 
class,  the  bright  stars  doubtless  average  nearer  to  us  than  the 
faint  ones ;  just  as  certainly  they  average  larger  in  diameter 
and  are  also  more  intensely  luminous.  But  when  we  compare 
a  single  bright  star  with  another  fainter  one  we  can  seldom  say 
to  which  of  the  three  different  causes  it  owes  its  superiority; 
or  that  a  particular  faint  star  is  smaller,  or  darker,  or  more 
distant  than  a  particular  bright  star,  unless  we  know  something 
beyond  the  simple  fact  that  it  is  fainter. 

566.   Dimensions  of  the  Stars. — We  have  very  little  absolute  Dimensions 
knowledge  on  this  subject ;  in  a  single  instance,  that  of  Algol  of  stars' 
(see    Sec.    582),  it   has   been   possible    to   obtain   an   indirect 
measure,  showing  that  that  particular  star  is  probably  some- 
what more  than  1  000000  miles  in  diameter  and  considerably 
bulkier  than  the  sun. 

The  apparent  angular  diameter  of  a  star  is  probably  in  no  Diameter 
case  large  enough  to  be  directly  measured  or  even  perceived  by  *°°  sma11 

*  +     for  micro- 

any  of  our  present  instruments.     At  the  distance  of  a  Centauri  metric 
the  sun's  apparent  diameter  would  be  somewhat  less  than  0".01.  measure- 

ment. 

In  the  case  of  binary  stars  of  which  we  happen  to  know  the 
parallax,  we  can  determine  their  masses,  but  diameters,  volumes, 
and  densities  are  at  present  quite  beyond  our  reach. 


516 


MANUAL   OF   ASTRONOMY 


Fraun- 
hofer's 
observations 
of  stellar 
spectra. 


Work  of 
Huggins 
and  Secchi. 


Secchi 's 
four  classes 
of  stellar 
spectra. 


STAR  SPECTRA 

567.  As  early  as  1824  Fraunhofer  observed  the  spectra  of  a 
number  of  bright  stars  by  looking  at  them  through  a  small 
telescope  with  a  prism  in  front  of  the  object-glass,  using  a  cylin- 
drical lens  in  the  eyepiece  to  widen  the  spectrum,  which  other- 
wise would  have  been  a  simple  streak  of  colored  light. 

In  1864,  as  soon  as  the  spectroscope  had  taken  its  place  as  a 
recognized  instrument  of  research,  it  was  applied  to  the  stars 
by  Huggins  and  Secchi.  The  former  studied  comparatively  few 
spectra  (especially  those  of  the  stars  a  Tauri  and  a  Orion  is), 
but  very  thoroughly,  with  reference  to  the  identification  of  their 
chemical  constituents.  He  found  with  certainty  in  their  spectra 
the  lines  of  sodium,  magnesium,  calcium,  iron,  and  hydrogen, 
and  more  or  less  doubtfully  a  number  of  other  metals.  Secchi, 
on  the  other  hand,  examined  a  great  number  of  stars  (nearly 
four  thousand),  less  in  detail,  but  with  reference  to  a  classifica- 
tion from  the  spectroscopic  point  of  view. 

568.  Secchi's  Classes  of  Spectra Secchi  divided  the  spectra 

into  four  classes,  as  follows : 

(I)  Those  which   have    a   spectrum  characterized   by  great 
intensity  of  the  hydrogen  lines,  which  look  very  much  like  H 
and  K  in  the  solar  spectrum,  all  other  lines  being  comparatively 
feeble  or  absent.     This  class  comprises  considerably  more  than 
half  of  all  the  stars  examined,  —  nearly  all  the  white  or  bluish 
stars;  Sirius  and  Vega  are  types.     (See  Fig.  184,  Sec.  571.) 

(II)  Those  which  show  a  spectrum  resembling  that  of  the  sun; 
i.e.,  characterized  by  numerous  fine  dark  lines  in  it,  due  to  the 
presence  of  metallic  vapors.     Capella  (a  Aurigse)  and  Pollux 
(yS  Geminorum)  are  conspicuous  examples.     The  stars  of  this 
class  are  also  numerous,  the  first  and  second  classes  together 
comprising    fully    seven    eighths    of    all    the    stars    observed. 
These  classes  shade  into  each  other,  however ;  certain  stars,  like 
Procyon  and  Altair,  seeming  to  be  intermediate  between  the  two. 


THE    LIGHT   OF   THE    STARS 


517 


(III)  About  five  hundred  stars  show  spectra  characterized  by 
dark  bands,  sharply  defined  at  the  upper  or  more  refrangible  edge 
and  shading  out  towards  the  red.     Most  of  the  red  stars,  and  a 
large  number  of  the  variable  stars,  belong  to  this  class,  and 
some  of  them  show  also  bright  lines  in  their  spectra;  a  Her- 
culis  may  be  taken  as  the  type.     (See  also  Fig.  186,  Sec.  578.) 

(IV)  This  class  comprises  a  comparatively  small  number  of 
faint  stars,  which  show,  like  the  preceding,  dark  bands,  but  shad- 
ing in  the  opposite  direction,  with  sometimes  a  few  bright  lines. 


H 


b    ~E 


II. 


III. 


Sinus 


CapeUa 


a  Orionis 


A  40     ' 


FIG.  181.  —  Secchi's  Types  of  Stellar  Spectra 

569.   The  typical  light  curves  of  the  four  classes  of  spectra  The  light 
are  represented  in  Fig.  181,  the  dark  lines  of  the  spectrum  curvesof 

the  differ- 

being  indicated  by  lines  running  downward  from  the  contour  ent  classes 
of  the  curve  and  the  bright  lines  by  lines  projecting  upward. 
Fig.  182,  from  photographs  by  Pickering,  gives  the  blue  and 
violet  portions  of  spectra  of  several  stars  ranging  from  the  first 
type  to  the  second. 

Pickering  has  proposed  a  fifth  class, — the  Wolf -Ray  et  stars, 
so  called, — containing  about  one  hundred  members,  which  have 


518  MANUAL   OF    ASTRONOMY 

a  peculiar  spectrum,  different  from  any  of  the  others,  and 
characterized  by  bright  lines.  All  of  them  are  found  in  or 
very  near  the  Milky  Way  or  in  the  two  "Nubeculse"  near  the 
south  pole. 

Vogel  uses  Secchi's  classification,  considerably  modified,  and 
Lockyer  has  proposed  an  entirely  new  one,  based  on  his  mete- 
oritic  hypothesis.  We  give  Secchi's,  however,  as  the  best  known 
and  lying  at  the  basis  of  the  more  recent  and  elaborate  classifi- 
cations by  Pickering  and  others.  A  classification  used  in  the 


Sirius 


Procyon 


Capella 


FIG.  182.  —  Star  Spectra 
Pickering 

recent  publications  of  Harvard  College  Observatory  recognizes 
ten  types,  designated  by  the  letters  0,  B,  A,  F,  G,  K,  M,  TV,  P,  Q. 
Photog-  570.   Photography  of  Stellar  Spectra.  —  The  observation  of 

8t^uar°f  ti1686  spectra  by  the  eye  is  very  tedious  and  difficult,  and  pho- 
spectra.  tography  has  been  brought  into  use  most  effectively.  Huggins 
in  England  and  Henry  Draper  in  this  country  were  the  pio- 
neers about  1880.  At  present  there  are  numerous  workers  in 
this  line  both  in  this  country  and  abroad,  and  the  method  has 
been  developed  to  high  perfection. 


THE   LIGHT   OF   THE   STARS  519 

All  but  a  few  stars  are  so  faint  that  satisfactory  visual  obser- 
vation of  their  spectra  is  impracticable,  but  photography  is 
nearly  independent  of  such  limitations,  for  with  sufficient  length 
of  exposure  the  sensitive  plate  records  whatever  falls  upon  it, 
however  feeble  the  light,  —  at  least  no  limits  are  at  present 
known. 

A  majority  of  observers  use  prismatic  spectroscopes  with  slit 
and  collimator  substantially  like  that  shown  in  Fig.  176.  With 
this  they  photograph  the  spectra  of  stars  separately,  one  by  one, 
each  on  a  little  plate  like  a  microscope  slide ;  with  the  star 
spectrum  is  also  photographed  a  reference  spectrum,  produced  by 
an  electric  spark  playing  between 
electrodes  of  known  metals. 

From  such  photographs  we  can 
measure  the  wave-length  of  lines 
in  the  star  spectra  and  the  shift 
of  the  lines,  if  any,  due  to  radial 
motion  and  recognize  the  con- 
stituent elements  of  the  star's 
atmosphere.  By  using  prisms 
of  quartz,  Sir  William  Huggins  \  Spectro- 

and    Lady  Huggins    have    been  ^  scope  with 


able  tO  Carry  their  investigations    FIG.  183. -Arrangement  of  the  Prisms 

J  in  the  Slitless  Spectroscope  prisms. 

with  great  success  into   the  in- 
visible ultra-violet  spectra  of  a  multitude  of  stars. 

571,   The  Slitless  or  Objective-Prism  Spectroscope — Professor  Thesiitiess 
Pickering  has  attained  his  wonderful  results  by  reverting  to  sPectr°- 
the  slitless  spectroscope,  arranged  in  the  manner  first  used  by 
Fraunhofer  and  later  revived  by  Secchi.     The  instrument  con- 
sists of  a  telescope  with  its  object-glass  corrected  for  the  photo- 
graphic instead  of  the  visual  rays,  equatorially  mounted  and 
carrying  outside  of  the  object-glass  one  or  more  objective  prisms 
having  a  refracting  angle  of  10°  to  30°,  each  large  enough  to 
cover  the  whole  lens. 


520 


MANUAL   OF   ASTRONOMY 


Its  advan- 
tages. 


Pickering  uses  ordinarily  an  11-inch  telescope,  formerly  belonging  to 
Draper,  or  a  14-inch  telescope,  with  a  battery  of  four  enormous  prisms 
placed  outside  of  the  object-glass,  as  shown  in  Fig.  183.  The  edges  of  the 
prisms  lie  east  and  west,  and  the  clockwork  on  the  telescope  is  adjusted  to 
go  a  little  too  fast  or  too  slow,  in  order  to  give  width  to  the  spectrum 
formed  upon  the  sensitive  plate,  which  is  placed  at  the  focus  of  the  object- 
glass  ;  if  the  clockwork  followed  the  star  exactly,  the  spectrum  would  be 
a  mere  narrow  streak. 

With  this  apparatus  and  an  exposure  of  from  ten  to  fifty  minutes, 
according  to  the  brightness  of  the  star,  spectra  are  obtained  which,  before 
enlargement,  are  fully  3  inches  long  from  the  F  line  to  the  ultra-violet 
extremity.  They  easily  bear  tenfold  enlargement  and  show  several  hun- 
dred lines  in  the  spectra  of  the  stars  belonging  to  the  second  or  solar  class. 


Its  disad- 
vantages. 


KH  h  Hy 

FIG.  184.  —  Photographic  Spectrum  of  Vega 

Fig.  184,  showing  the  spectrum  of  Vega,  is  from  one  of  these  photographs, 
and  the  spectra  of  Fig.  182  are  enlarged  from  plates  made  with  the  same 
instrument. 

The  great  Bruce  telescope  at  Arequipa  (Sec.  536)  has  also  been  provided 
with  an  object-glass  prism,  and  so  has  the  McClean  telescope  at  the  Cape 
of  Good  Hope;  with  both  these  instruments  the  spectra  of  very  faint 
stars  can  now  be  photographed. 

572.  Advantages  and  Disadvantages  of  the  Slitless  Spectro- 
scope. —  It  has  three  great  advantages :  first,  that  it  utilizes  all 
the  light  which  comes  from  the  star  to  the  object-glass,  much  of 
which,  in  the  usual  form  of  instrument,  is  lost  in  the  jaws  of  the 
slit;  second,  by  taking  advantage  of  the  length  of  a  large  tele- 
scope, it  produces  a  very  high  dispersion  with  even  a  single  prism  ; 
third,  and  most  important  of  all,  it  gives  on  the  same  plate  and 
with  a  single  exposure  the  spectra  of  all  the  many  stars  (some- 
times more  than  a  hundred)  whose  images  fall  upon  the  plate. 

On  the  other  hand,  the  giving  up  of  the  slit  precludes  all  the 
usual  methods  of  identifying  the  lines  oi  a  spectrum  by  actually 


THE   LIGHT   OF   THE   STARS  521 

confronting  it  with  comparison  spectra,  and  makes  it  impossible 
to  use  the  instrument  for  measuring  the  shift  of  spectrum  lines 
and  thus  determining  the  "radial  motion"  of  a  star.  Nor  can 
it  be  used  to  study  the  spectrum  of  an  object  of  sensible  extent, 
like  a  planet  or  a  nebula. 

Moreover,  it  gives  well-defined  spectra  only  when  the  air  is 
very  steady  and  the  star  images  quiescent, —  a  condition  of 
comparatively  little  importance  with  a  slit  spectroscope,  since 
atmospheric  disturbance,  with  such  an  instrument,  does  not 
affect  the  distinctness  of  the  spectrum  photographed,  but  only 
makes  it  necessary  to  give  a  longer  exposure. 

Of  course,  too,  the  enormous  prisms  make  the  slitless  spectro- 
scope very  costly. 

For  what  may  be  called  the  "reconnaissance,"  or  classification  Admirable 
of  star  spectra  by  the  thousands,  the  slitless  spectroscope  stands 
unrivaled  and  is  effective  for  the  study  of  one  class  of  spectro- 
scopic  binaries  (Sec.  593),  in  which  the  lines   of  the  spectra 
double  and  undouble  themselves. 

With  instruments  of  this  kind  at  Cambridge  and  Arequipa, 
the  Cambridge  observers  have  already  obtained  and  stored  away 
the  photographic  spectra  of  at  least  one  hundred  thousand 
stars  and  have  issued  one  great  catalogue  of  spectra  (the  Draper 
Catalogue),  soon  to  be  followed  by  others.  It  should  be  men- 
tioned that  the  funds  for  the  prosecution  of  these  spectroscopic 
researches  by  Professor  Pickering  have  been  mainly  provided 
by  Mrs.  Draper,  as  a  memorial  of  her  husband,  Professor  Henry 
Draper,  the  American  pioneer  in  stellar  spectroscopy. 

It  is  impracticable  in  a  text-book  like  the  present  to  deal  with  the 
interesting  and  important  details  of  stellar  spectra  as  revealed  by  photog- 
raphy. For  these  the  student  must,  for  the  present,  be  referred  to  the 
various  publications  which  contain  the  results  of  the  observers. 


522 


MANUAL    OF   ASTRONOMY 


Classes  of 

variable 

stars. 


Gradual 
changes  of 
certain 
stars. 


VAEIABLE   STAKS 

573.  Many  stars  change  their  brightness  more  or  less  and  are 
known  as  variable.     They  may  be  classified  as  follows : 

A.    NON-PERIODIC  VARIABLES 

(I)  Stars  that   change    their   brightness    slowly   and    con- 
tinuously. 

(II)  Those  that  fluctuate  irregularly. 

(III)  "Temporary  stars,"  or  "Novae,"  which  blaze  out  sud- 
denly and  then  disappear. 

B.    PERIODIC  VARIABLES 

(IV)  Variables  of  the  type  of  o  Ceti,  usually  having  a  period 
of  several  months. 

(V)  Variables  of  the  type  of  /3  Lyrse,  usually  having  short 
periods. 

(VI)  Variables  of  the  "Algol  type,"  in  which  the  variation 
is  like  what  would  be  produced  if  the  star  were  periodically 
eclipsed  by  some  intervening  object. 

NON-PERIODIC   VARIABLES 

574,  Class  I:  Gradual  Changes. — The  number  of  stars  posi- 
tively known  to  be  gradually  changing  in  brightness  is  surpris- 
ingly small,  considering  that  all  are  growing  older.      On  the 
whole,  the  stars  present,  not  only  in  position,  but  in  bright- 
ness also,  sensibly  the  same  relations  as  in  the  catalogues  of 
Hipparchus  and  Ptolemy. 

There  are,  however,  instances  in  which  it  is  almost  certain 
that  considerable  change  has  occurred,  even  within  the  last  two 
or  three  centuries.  In  the  time  of  Eratosthenes  the  star  in  the 
claw  of  the  Scorpion  (now  /3  Libras)  was  reckoned  as  the  bright- 
est in  the  constellation.  At  present  it  is  a  whole  magnitude 
below  Antares,  which  is  now  much  superior  to  any  other  star 
in  the  vicinity.  So  when  the  two  stars,  Castor  and  Pollux,  in 


THE   LIGHT   OF   THE   STARS  523 

the  constellation  Gemini,  were  lettered  by  Bayer  in  1610,  the 
former,  a,  was  certainly  not  inferior  to  Pollux,  which  was 
lettered  /3,  but  is  now  distinctly  the  brighter.  Taking  the 
whole  heavens,  we  find  a  number  of  such  cases,  perhaps  a  dozen 
or  more. 

It  is  commonly  believed  that  a  considerable  number  of  stars  have  disap- 
peared since  the  early  catalogues  were  made,  and  that  some  new  ones  have 
come  into  existence.  While  it  is  unsafe  to  deny  absolutely  that  such 
things  may  have  happened,  we  can  say,  on  the  other  hand,  that  not  a 
single  case  of  the  kind  is  certain.  In  numerous  instances  stars  recorded 
in  the  catalogues  are  now  doubtless  missing ;  but  in  nearly  every  case  the 
loss  can  be  accounted  for,  either  as  an  error  of  observation  or  printing,  or 
by  the  fact  that  the  stars  observed  were  asteroids.  There  is  not  a  single 
case  on  record  of  a  new  star  appearing  and  remaining  permanently  visible, 
nor  of  the  certain  disappearance  of  any,  except  the  few  so-called  "  tem- 
porary stars." 

Class  II :   Irregular   Fluctuations The  most  conspicuous  stars  that 

variable  star  of  this  class  is  ??  Argus  (or  77  Carinse),  a  star  not  fluctuate 

irregularlv. 

visible  in  the  United  States.  It  varies  all  the  way  from  zero 
magnitude  (which  it  had  in  1843,  when  it  stood  next  to  Sirius 
in  brightness)  down  to  the  seventh,  which  has  been  its  status 
since  1865,  although  in  1888  it  was  for  a  time  reported  as 
slightly  increasing. 

a  Orionis  and  a  Cassiopeise  behave  in  a  similar  way,  except 
that  their  range  of  brightness  is  small,  not  much  exceeding  half 
a  magnitude.  About  forty  or  fifty  other  stars  belong  to  the 
same  class,  —  at  least  no  regular  periodicity  has  yet  been  found 
in  their  variations. 

575,    Class  III :    Temporary  Stars.  —  There   are  more  than  Temporary 
twenty  well-authenticated  instances  (and  several  others  which  stars» or 
are  doubtful)  of  stars  which  have  shone  out  suddenly  and  then 
gradually  faded  away. 

The  most  remarkable  of  them  was  that  known  as  "  Tycho's  Tycho's  star 
star,"   which  appeared  in   the    constellation  of  Cassiopeia  in  ° 
November,  1572,  was  for  some  days  as  bright  as  Venus  at  her 


524 


MANUAL   OF   ASTRONOMY 


Nova 
Coronae  of 
1866. 


best  (visible  in  the  daytime),  and  then  gradually  waned,  until  at 
the  end  of  sixteen  months  it  became  invisible,  for  there  were  no 
telescopes  then.  It  is  not  certain  whether  it  still  exists  as  a 
telescopic  star ;  so  far  as  we  can  judge,  it  may  be  any  one  of 
several  which  are  near  the  place  determined  by  Tycho. 

There  has  been  a  curious  and  utterly  unfounded  notion  that  this  star 
was  the  "  Star  of  Bethlehem,"  and  would  reappear  to  herald  the  second 
advent  of  the  Lord. 

Kepler's  Another  temporary  star  was  observed  by  Kepler  in  1604, 

star  of  1604.  w}1{c]1  for  some  weeks  was  as  bright  as  the  planet  Jupiter,  and 
remained  visible  for  nearly  two  years. 

A  temporary  star,  which  appeared  in  the  constellation  of 
Corona  Borealis  between  the  10th  and  12th  of  May,  1866,  is 
interesting  as  having  been  the  first  to  be  studied  by  the  spec- 
troscope. When  near  its  brightest  (second  magnitude)  it  was 
examined  by  Huggins,  and  then  showed  the  same  bright  lines 
of  hydrogen  which  are  conspicuous  in  the  solar  prominences. 
Before  its  outburst  it  was  an  eighth-magnitude  star  of  Arge- 
lander's  catalogue,  and  within  a  few  months  it  returned  to  its 
former  state,  which  it  still  retains. 

In  1876  another  second-magnitude  star  appeared  on  Novem- 
ber 24  in  Cygnus,  and  according  to  its  observer,  Schmidt  of 
Athens,  rose  from  invisibility  to  the  second  magnitude  within 
four  hours,  remained  at  its  maximum  for  only  a  day  or  two,  and 
faded  away  to  below  the  sixth  magnitude  within  a  month.  It 
still  exists  as  a  very  minute  telescopic  star  of  the  fifteenth 
magnitude.  This  also  was  spectroscopically  studied  by  several 
observers  (by  Yogel,  especially)  with  the  remarkable  result  that 
the  spectrum,  which  at  the  maximum  was  nearly  continuous, 
though  marked  by  the  bright  lines  of  hydrogen  and  by  bands  of 
other  unknown  substances,  at  last  became  a  simple  spectrum  of 
three  bright  lines  like  that  of  a  nebula  (Sec.  602). 

In  August,  1885,  a  sixth-magnitude  star  suddenly  appeared 


Nova 

Cygni, 

1876. 


THE   LIGHT   OF   THE   STARS 


525 


in  the  great  nebula  of  Andromeda,  very  near  its  nucleus.     The  Nova 
star  began  to  fade  almost  immediately  and  in  a  few  months 
entirely  disappeared.     Its   spectrum   was  sensibly  continuous, 
without  lines  of  any  sort. 

576.   Nova  Aurigae.  —  In  December,  1891,  a  "Nova,"  shown  Nova 
in  photographs,  though  not  seen  by  any  one  until  Jan.  30,  1892,   Aurlsae» 
appeared  in  the  foot  of  Auriga.     Early  in  February  it  was  very 
nearly  of  the  fourth  magnitude,  and  remained  visible  to  the  naked 
eye  for  about  a  month.     Its  spectrum  was  carefully  studied,  both 
visually  and  photographically,  and  was  very  interesting.     The 
bright  lines  were  numerous,  those  of  hydrogen  and  helium, 


K    H 


FIG.  185.  —  Spectrum  of  Nova  Aurigae 

with  the  H  and  K  of  calcium,  being  specially  conspicuous ;  and 
each  of  them  was  accompanied  by  a  dark  line  on  the  more  refran- 
gible side,  as  if  two  bodies  were  concerned ;  one  of  them  giving 
bright  lines  in  its  spectrum  and  receding  from  us,  the  other  with 
corresponding  dark  lines  in  its  spectrum,  but  approaching. 
Fig.  185  is  from  a  photograph  made  at  Potsdam.  According 
to  Yogel,  the  relative  velocity  of  the  two  masses  must,  if  this  is 
the  true  explanation,  have  exceeded  550  miles  a  second. 

A  slightly  different  explanation,  suggested  by  Lord  Kelvin,  is 
that  the  high  velocity  indicated  is  not  that  of  the  large  masses 
which  collide,  but  of  small  fragments  and  particles,  "  spattered 
off,"  so  to  speak,  by  the  impact. 

On   the   whole,   it    now,   however,   seems    somewhat    more 


Twin  lines 
of  hydrogen 
bright  and 
dark. 


Question 
whether  the 
doubling  is 
explained 
by  Doppler's 
principle. 


526  MANUAL   OF    ASTRONOMY 

probable  that  the  displacement  and  widening  of  the  lines  is  to 
be  explained  by  violent  pressure,  on  the  principle  discovered  by 
Humphreys  and  Mohler  (Sec.  256),  rather  than  by  the  Doppler- 
Fizeau  principle.  The  phenomena  then  would  appear  to  be  a 
result  of  explosion  instead  of  collision,  as  has  been  very  generally 
assumed,  —  something  very  analogous  to  the  phenomena  which 
accompany  the  eruptive  prominences  ejected  from  the  sun. 

In  April  the  star  became  invisible,  but  slightly  brightened 
again  in  the  autumn,  and  then  showed  an  entirely  different 
spectrum,  closely  resembling  that  of  a  nebula.  (See  Fig.  203, 
Sec.  602.)  In  this  figure  all  but  the  lower  line  are  photographs 
of  small  nebulse  made  with  a  "  slitless  spectroscope  "  (Sec.  571), 
so  that  each  of  the  images  of  the  nebula  corresponds  to  what 
would  be  a  "  bright  line  "  in  its  spectrum,  if  a  spectroscope 
with  a  slit  had  been  used.  The  lowest  line  is  the  photograph 
of  the  star  made  by  the  same  instrument.  Finally,  however 

its  spectrum  (January,  1902),  its    spectrum,   according    to   photographs    of 
Campbell,  has  become   continuous,  the   nebula  having  appar- 

finaiiy  con-    ently  reverted  to  the  original  condition  of  a  star.     At  present 

tinuous.         it  is  Of  the  thirteenth  magnitude. 

The  behavior  of  this  star  has  led  to  a  great  deal  of  discussion 
and  cannot  be  said  to  have  reached  as  yet  a  wholly  satisfactory 
explanation. 

The  still  more  recent  Novae  of  1893,  1895,  and  1898,  all  of  them  in 

Photo-  the  southern   hemisphere,   are    peculiar   in    that    they  were   detected  by 

graphic  photography,  having  been  recognized  by  Mrs.   Fleming  of   the   Harvard 

Nova.  College  Observatory,  both  upon  the  chart  plates  and  spectrum  photographs 

taken  at  the  Arequipa  station  in  South  America.     The  stars  were  hardly 

large  enough  to  be  seen  by  the  naked  eye,  and  there  is  no  record  of  their 

visual  observation,  but  their  photographic  spectra  appear  to  be  identical 

with  that  of  Nova  Aurigse.     It  now  seems  rather  probable  that  "  new 

stars  "  are  not  really  extremely  rare,  and  it  is  clear  that  there  are  important 

physical  resemblances  between  them. 

577,  Nova  Persei.  —  A  very  recent  instance  of  a  new  star, 
and  one  of  the  most  remarkable,  is  that  of  the  star  which  first 


THE   LIGHT   OF   THE   STARS  527 

appeared,  probably  on  Feb.  20,  1901,  but  was  first  seen  on  the  Nova  Persei 
21st,  having  then  about  the  brightness  of  the  pole-star. 

Photographs  of  the  region  containing  the  star,  taken  at  the 
Harvard  College  Observatory  on  several  dates  previous  and  up  to 
the  19th,  show  that  on  the  19th  the  star  had  not  yet  appeared, 
or  at  least  had  not  reached  a  magnitude  above  the  twelfth. 

It  increased  in  brightness  at  least  2'50 00-fold  within  three  Rapid  in- 
days,  and  on  the  22d  it  was  for  a  few  hours  the  brightest  star  crease  of 

J  brightness. 

in  the  heavens,  Sirius  alone  excepted,  having  attained  very 
nearly  the  zero  magnitude,  —  the  most  brilliant  Nova  since 
Kepler's  star  of  1604.  Its  rise  was  extremely  rapid,  and  its 
descent  was  also  swift  as  compared  with  that  of  Kepler's  star, 
for  it  faded  rapidly,  so  that  by  the  end  of  March  it  was  barely 
visible  to  the  eye. 

The  spectrum,  as  photographed  at  Cambridge  on  the  22d,  was  quite   Its  spectrum 
unlike  that  of  Nova  Aurigae  and  most  other  new  stars,  resembling  the    during  the 
spectrum  of  J3  Orionis  (Rigel),  —  mainly  continuous,  but  crossed  by  more   e 
than  thirty  not  very  conspicuous   dark  lines.     Clouds   prevented  further 
spectrographs  until  the  24th,   and   then   a   great   change    had  occurred. 
The  bright  lines  of  hydrogen,  with  their  dark  correlatives,  were  now  con- 
spicuous, just  as  they  were  in  the  spectrum  of  Nova  Aurigae  (Fig.  185). 

Since  then  the  star  has  followed  the  usual  course;   its  spectrum  has 
become  nebular  and  still  continues  so  (January,  1902),  though  with  some    Spectrum 
non-nebular  peculiarities    in  the  breadth   of    the   nebular   lines   and    the    becomes 
presence  of  other  conspicuous  lines  not  found  in  nebulae. 

During  its  decline  its  brightness  oscillated  capriciously  more  than  a   Oscillations 
whole  magnitude,  the  irregular  interval  between  the  maxima  increasing   of  bright- 
from  about  two  days  in  February  to  six  or  eight  in  the  autumn,  when  it  ness* 
had  fallen  to  the  limit  of  unaided  vision. 

In  September  it  became  possible  to  photograph  the  invisible  surrounding 
nebulosity  with  the  reflecting  telescopes  (not  with  the  great  refractors)  of   Nebulosity 
the  Lick  and  Yerkes  observatories.     It  was  found  to  be  very  extensive,   photo- 
roughly  circular,  with  an  apparent  diameter  about  half  that  of  the  moon ;    gra] 
and  since  the  Nova  shows  no  sensible  proper  motion  or  parallax,  making 
it  certain  that  its  distance  is  greater  than  that  of  the  nearer  stars,  the  real   Its  enormous 
diameter  of  the  nebula  must  be  at  least  fifteen  hundred  times  the  diameter  dimensions, 
of  the  earth's  orbit ;  probably  this  is  an  extreme  underestimate. 


528 


MANUAL   OF   ASTRONOMY 


There  are  several  pretty  well  marked  knots  of  condensation  in  the 
nebula,  and  the  comparison  of  photographs  made  at  different  dates  shows 
that  these  are  moving  away  from  the  center  at  various  rates,  averaging 
about  1'  in  six  weeks,  —  a  motion  not  apparently  very  rapid  seen  from  the 
earth,  but  really  not  less  than  2000  miles  a  second,  if  the  Nova  is  as  near 
as  a  Centauri.  Very  probably  it  is  ten  to  a  hundred  times  more  distant,  or 
even  remoter  yet.  Observations  show  no  sensible  parallax. 

Kapteyn  suggests  that  the  apparent  motion  is  simply  the  progressive 
illumination  of  spiral  streams  of  nebulosity  advancing  along  them  with 
the  velocity  of  light,  the  object  being  some  300  light-years  distant. 


PERIODIC   VARIABLES 

578.   Class  IV:  Variables  of  the  "  Omicron  Ceti"  Type.- 

These  objects  behave  almost  exactly  like  the  temporary  stars  in 
remaining  most  of  the  time  faint,  rapidly  brightening,  and  then 
gradually  fading  away ;  but  they  do  it  periodically,  o  Ceti,  or 
Mira  (i.e.,  "the  wonderful"),  is  the  type.  It  was  discovered 

by  Fabricius  in  1596, 
and  was  the  first  vari- 

F.G.  186. -Spectrum  of  Mira  Ceti  ^^     reoognized    as 

such.  During  most  of  the  time  it  is  invisible  to  the  naked  eye, 
of  about  the  ninth  magnitude  at  the  minimum ;  but  at  intervals 
of  about  eleven  months  it  runs  up  to  the  fourth  or  third,  or 
even  second,  magnitude,  and  then  back,  the  rise  being  much 
more  rapid  than  the  fall.  It  remains  at  its  maximum  about  a 
week  or  ten  days. 

The  maximum  brightness  varies  very  considerably;  and  its 
period,  while  always  about  eleven  months,  also  varies  to  the 
extent  of  two  or  three  weeks,  and  during  the  last  few  years 
seems  to  have  shortened  materially.  The  spectrum  of  the  star 
at  its  maximum  is  very  beautiful,  showing  a  large  number  of 
intensely  bright  lines  (some  of  which  are  certainly  due  to 
hydrogen)  superposed  upon  a  fine  banded  spectrum  of  Secchi's 
third  class  (Fig.  186,  photographed  by  Pickering). 

Its  "  light  curve  "  is  A  in  Fig.  187. 


THE   LIGHT   OF   THE   STARS 


529 


A  large  proportion  of  the  known  variables  belong  to  this 
class  (nearly  half  of  the  whole),  and  a  large  percentage  of  them 
have  periods  which  do  not  differ  very  widely  from  one  year. 
None  so  far  discovered  exceed  two  years,  and  none  are  less  than 
two  months.  Most  of  the  periods,  however,  are  more  or  less 
irregular. 

579,  Class  V :  Short-Period  Variables.  —  In  these  the  periods  short-period 
range  from  about  three  hours  (that  of  a  little  star  m  Cygnus,  variables  of 
detected  at  Moscow  in  1904)  to  three  or  four  weeks,  and  the 


FIG.  187.  —  Light  Curves  of  Periodic  Variables 

light  of  the  star  fluctuates  continually.  In  many  cases  there 
are  two  or  more  maxima  in  a  complete  period,  accompanied  by 
complicated  spectroscopic  phenomena  much  like  those  observed 
in  Nova  Aurigse.  The  light  curves  of  j3  Lyrse  and  77  Aquilse, 
which  are  typical  of  this  class,  are  given  at  B  (Fig.  187). 


530 


MANUAL   OF    ASTRONOMY 


580.  Class  VI:    the  Algol  Type.  —  In   this    class   the   star 
remains  bright  for  most  of  the  time,  but  apparently  suffers  a 
periodical  eclipse.     The  periods  are  mostly  very  short,  ranging 
from  ten  hours  to  about  five  days. 

Algol,  or  (S  Persei,  is  the  type  star.  Usually  it  is  of  the 
second  magnitude,  and  it  loses  about  five  sixths  of  its  light  at 
the  time  of  obscuration.  The  fall  of  brightness  occupies  about 
four  and  one-half  hours ;  the  minimum  lasts  about  twenty  min- 
utes, and  the  recovery  of  light  takes  about  three  and  one-half 
hours.  The  period,  a  little  less  than  three  days,  is  known  with 
great  precision,  —  to  less  than  a  single  second  indeed,  —  and  is 
given  in  connection  with  the  light  curve  of  the  star  in  Fig.  187. 
About  ninety  stars  of  this  class  are  known  at  present. 

581,  Explanation  of  Variable  Stars.  —  No  single  explanation 
will  cover  the  whole  ground.      As  to  progressive  changes,  none 
need  be  looked  for.     The  wonder  rather  is  that  as  the  stars 
grow  old  such  changes  are  not  more  notable.     As  for  irregular 
changes,  110  sure  account  can  yet  be  given.     Where  the  range 
of  variation  is  small  (as  it  is  in  most  cases)  one  thinks  of  spots 
on  the  surface  of  the  star,  more  or  less  like  sun-spots  ;  and  if 
we  suppose  these  spots  to  be  much  more  extensive  and  numer- 
ous than  are  sun-spots,  arid  also  like  them  to  have  a  regular 
period  of  frequency,  and  also  that  the  star  revolves  upon  its 
axis,  we  find  in  the  combination  a  possible  explanation  of  a 
large  proportion  of  all  the  variable  stars.     For  the  temporary 
stars  we  may  imagine  either  great  eruptions  of  glowing  mat- 
ter,  like    solar   prominences   on    an    enormous   scale,   or,  with 
Mr.  Lockyer,  we  may  imagine  that  most  of  the  variable  stars 
are  only  swarms  of  meteors,  rather  compact,  but  not  yet  having 
obtained  the   condensed   condition  of  our  sun.     Stars  of  the 
Mira  type,  according  to  his  view,  owe  their  regular  outbursts 
of  brightness  to  the  collisions  due  to  the  passage  of  a  smaller 
swarm  through  the  outer  portions  of  a  larger  one,  around  which 
the  smaller  revolves  in  a  long  ellipse. 


THE   LIGHT    OF    THE   STARS  531 

But  the  great  irregularity  in  the  periods  of  variables  belong- 
ing to  this  class  is  hard  to  reconcile  with  a  true  orbital  revo- 
lution, which  is  usually  an  accurate  timekeeper. 

Many  of  the  spectroscopic  phenomena  of  the  temporary  stars 
and  of  the  periodic  stars  of  Class  IV  resemble  pretty  closely 
those  that  appear  in  the  solar  chromosphere  and  prominences, 
suggesting  in  such  cases  a  theory  of  explosion  or  eruption. 

In  the  case  of  the  short-period,  "  punctual "  variables,  as  Miss  Short-period 
Clerke   calls   them,  of   Class  V,  the  spectroscopic  phenomena  variations 

1  due  to  revo- 

m  some  instances  seem  to  indicate  the  mutual  interaction  of  iution  of 
two  or  more  bodies  revolving  close  together  around  a  common  stellar 
center   of   gravity ;    this   is   certainly  the   case   with   ft  Lyrse. 
(See  Sec.  592.)     Others  admit  of  simpler  explanation,  as  due 
merely  to  the  axial  rotation  of  a  body  with  large  spots  upon  its 
surface. 

582.   Stellar  Eclipses.  —  As  to  stars  of  the  Algol  type,  the  stellar 
most  natural  explanation,  suggested  by  Goodricke  more  than  a  ecllPses- 
century  ago,  is  that  the  obscuration  is  an  eclipse  produced  by 
the  periodical  interposition  of  some  opaque  body  between  us 
and  the  star. 

The  truth  of  this  theory  was  substantially  demonstrated  in  vogei's 
1889  by  Vogel,  who  found  by  his  spectroscopic  observations  resultsasto 
(see  Sec.  542)  that  seventeen  hours  before  the  minimum  Algol  Of  Algol, 
is  receding  from  us  at  the  rate  of  nearly  27  miles  a  second, 
while  seventeen  hours  after  the  minimum  it  is  coming  toward 
us    at  practically  the    same   rate.      This    is    just  what  ought 
to  happen  if  Algol  had  a  large  dark  companion  and  the  two 
were  revolving  around  their  common  center  of  gravity,  in  an 
almost   circular    orbit,    nearly    edgewise    towards    the    earth. 
Vogei's  conclusions  are  that  the  distance  of  the  dark  star  from 
Algol  is  about  3  250000  miles,  and  that  their  diameters  are 
about  840000  and  1  060000  miles,  respectively.     Furthermore, 
their  period  being  2d20h48m.9,  it  follows  (Sec.  594)  that  their 
united  mass  is  about  two  thirds  that  of  the  sun,  and  their  mean 


532 


MANUAL   OF   ASTRONOMY 


Number  of 
variables. 


Their  desig- 
nation. 


density  only  about  one  fifth  as  great  as  his,  less  even  than  that 
of  Saturn,  and  not  much  above  the  density  of  cork.  Fig.  188 
represents  the  system  as  described  by  Vogel,  the  common  center 
of  gravity  being  at  (7,  around  which  both  stars  revolve,  always 
keeping  opposite  each  other. 

In  the  case  of  Y  Cygni  both  components  are  about  equally 
bright,  so  that  two  minima  occur  at  each  revolution,  but  not  at 

equal  intervals. 
Duner  has  shown 
that  this  can  be  ex- 
plained by  the  ellip- 
tical form  of  the  two 
orbits  described 
N      around   the    common 
/      center. 

583.  Number  and 
Designation  of  Vari- 
ables and  their  Range 
of  Variation.  —  Mr. 
Chandler's  catalogue 
of  known  variables 
(published  in  1896) 
included  393  objects, 
besides  also  a  con- 
siderable number  of 
suspected  variables. 

About  three  hundred  of  them  are  clearly  periodic  in  their  varia- 
tion. The  rest  of  them  are,  some  irregular,  some  temporary,  and 
in  respect  to  many  we  have  not  yet  certain  knowledge  whether 
the  variation  is  or  is  not  periodic.  Since  1896  the  number  has 
rapidly  increased,  and  now  (1909)  is  over  4000. 

Such  variable  stars  as  had  not  familiar  names  of  their  own 
before  the  discovery  of  their  variability  are  generally  indicated 
by  the  letters  R,  S,  T,  etc.;  i.e.,  R  Sagittarii  is  the  first 


To  Earth 


FIG.  188.  — System  of  Algol 


THE   LIGHT   OF   THE    STARS  533 

discovered  variable  in  the  constellation  of  Sagittarius ;  S  Sagit- 
tarii  is  the  second,  and  so  on. 


In  a  considerable  number  of  the  earlier  discovered  variables  the  range 
of  brightness  is  from  two  to  eight  magnitudes,  i.e.,  the  maximum  bright-  Range  of 
ness  exceeds  the  minimum  from  six  to  a  thousand  times.    In  the  majority,   brightness, 
however,  the  range  is  much  less,  —  often  only  a  fraction  of  a  magnitude. 
A  large  proportion  of  the  variables,  especially  of  Classes  IV  and  V,  are 
reddish  in  their  color.    This  is  not  true  of  the  Algol  type. 

Photography  has  lately  come  to  the  front  as  a  most  effective  method  of 
detecting  variables.  A  very  large  proportion  of  all  those  discovered  within 
the  last  dozen  years  have  been  found  by  the  study  of  the  photographic 

star  charts  made  at  the  Harvard  Observatory  and  its  South  American  Detection  of 

,  ,    ,    variables 

stations.    In  many  cases  the  photographed  spectrum  ot  a  star  nas  attracted  ,     photog- 

attention  by  its  bright  lines  and  a  peculiar  «  colonnaded  "  structure,  mark-  raphy. 
ing  it  as  "  suspicious  "  ;  and  the  suspicion  is  usually  soon  confirmed.     In 
several   cases  large   numbers  of  variables  have  lately  been  found   near 
together,  —  21  near  y  Aquilae,  117  in  the  greater  Magellanic  cloud,  70  in 
the  nebula  of  Orion.    They  are  nearly  all  extremely  small. 

584.  Variable-Star  Clusters.  —  One  of  the  most  interesting 
recent  results  of  stellar  photography  is  the  discovery  of  variable- 
star  dusters,  announced  by  Pickering  in  1895,  from  the  study 
of  photographs  made  by  Prof.  S.  I.  Bailey  at  Arequipa.  A  Variable 

large  number  of  negatives  of  several  different  clusters  were  starsmstar- 

clusters, 
made,  and  it  soon  appeared  that  while  in  some  no  changes  were 

apparent,  in  others  variable  stars  abound.  In  1898  Professor 
Pickering's  census  stood  as  follows  :  in  the  cluster  known  as 
3  Messier  (in  the  constellation  of  the  "  Hunting  Dogs  ")  no 
less  than  132  stars  had  been  found  to  be  variable,  out  of  about 
900  which  can  be  counted  in  the  cluster;  in  the  cluster  known 
as  &>  Centauri  (Fig.  195,  Sec.  598)  there  were  122  ;  in  5  Messier 
(Libra)  (Fig.  189),  85;  in  the  cluster  known  as  N.  G.  C. 
7078,  51,  and  47  more  in  three  or  four  other  clusters,  —  437  in 
all.  Since  then  the  number  has  been  continually  increasing 
with  further  observations,  and  already  it  probably  stands  above 


534  MANUAL   OF   ASTRONOMY 

500.     In  many  clusters   (and  even  in  the   majority)   equally 
bright  with  these  not  a  single  variable  has  yet  been  found. 
Rapidity  The  periods  generally  range  from  ten  to  fourteen  hours,  the 

and  range  of  averaore  being  about  twelve  and  one  half.     The  range  of  bright- 
variation. 

ness  is  usually  from  one  to   two  magnitudes,   and  the  light 

curves  resemble  that  of  o  Ceti,  the  rise  being  more  abrupt  than 
the  descent.  Photographs  of  some  of  these  clusters,  taken  at 
an  interval  of  only  an  hour  or  two,  show  numerous  cases  where 
the  change  amounts  to  a  full  magnitude. 


FIG.  189.  —Variable-Star  Cluster,  5  M  Librae 

Fig.  189  is  from  two  such  Arequipa  photographs  of  5  Messier,  taken 
two  hours  apart,  and  the  little  arrows  point  out  some  of  the  stars  which 
have  changed  their  brightness  in  that  short  time.  The  stars  of  the  cluster 
are  mostly  below  the  eleventh  or  twelfth  magnitude. 

In  Table  VI  of  the  Appendix  we  give  from  Chandler's  cata- 
logue a  list  of  the  principal  naked-eye  variables  which  can  be 
seen  in  the  United  States. 

The  observation  of  variables  is  especially  commended  to  the  attention 
oi  amateurs,  because,  with  a  very  scanty  instrumental  equipment,  work  of 
real  scientific  value  can  be  done  in  this  line.  It  was  an  amateur  (the  Rev. 
Dr.  Anderson  of  Edinburgh)  who  first  announced  both  Nova  Aurigse  and 
Nova  Persei.  The  observer  should  put  himself  in  communication  with 
the  director  of  some  active  observatory,  in  order  to  secure  the  proper  dis- 
cussion and  publication  of  his  results. 


THE   LIGHT   OF   THE   STARS  535 


EXERCISES 

1.  What  is  the  brightness  of  a  star  of  the  10.5  magnitude  (on  the  abso- 
lute scale)  compared  with  that  of  a  star  of  the  standard  first  magnitude  ? 

Solution.  From  Sec.  558,  equation  (1),  we  have  log  610.5  =  log  &i  —  T4o  x  9.5. 
If  we  take  the  brightness  of  the  first-magnitude  star  as  the  unit  of  brightness, 
log  61  =  0,  and  we  have  log  &i0.5  =  0  -  0.4  X  9.5  =  -  3.8000.  To  bring  this 
entirely  negative  logarithm  into  the  usual  tabular  form,  in  which  the  character- 
istic only  is  negative  while  the  mantissa  is  positive,  we  numerically  increase 
the  characteristic  by  unity,  making  it  —  4,  and  at  the  same  time  take  for  the 
new  mantissa  1-0.8000,  or  .2000;  we  have,  therefore,  log  610.5  =  4.2000 ; 
whence,  from  the  logarithmic  table,  we  find  610.5  =  0.000158. 

Ana.   610.5  =  0.000158. 

Also  log  ~  =  0  -  (  -  3.8000)  =  +  3.8000 ;  whence, 

"105 

Ans.   61  =  6309.6  x  610.5. 

(In  all  computations  respecting  stellar  magnitudes  four-place  tables  are 
sufficient.) 

2.  What  is  the  brightness  of  an  eleventh-magnitude  star  in  terms  of 
the  first?  AnSt   o.OOOl,  or  y^. 

3.  What  is  the  brightness  of  a  4.8-magnitude  star  in  terms  of  the  first? 

Ans.    0.0302,  or  T^I- 

4.  What  is  the  magnitude  of  a  star  whose  brightness  is  ^foro  tna*  °f  a 
first-magnitude  star?     (Sec.  558,  equation  (2).)         AnSt    13.5  magnitude. 

5.  What  is  the  magnitude  of  a  star  a  millionth  as  bright  as  a  first- 
magnitude  star?  ^m>    16th  magnitude. 

6.  What  is  the  magnitude,  on  the  absolute  scale,  of  a  luminary  80000- 
000000  times  as  bright  as  a  first-magnitude  star  ?     (log  80000  000000  = 
10.9031.) 

Ans.    —  26.26  magnitude.     (This  is  about  the  estimated  brightness 
of  the  sun.) 

7.  What  is  the  apparent  magnitude  of  a  double  star  whose  components 
are  of  the  first  and  second  magnitudes,  respectively  ? 

Ans.    0.64  magnitude. 

8.  What,  if  the  components  are  of  the  second  and  fourth  magnitudes? 

Ans.    1.85  magnitude. 

9.  If  the  distance  of  a  fourth-magnitude  star  were  diminished  one 
half,  of  what  magnitude  would  it  appear?  AnSt   2.50  magnitude. 


536 


MANUAL   OF   ASTRONOMY 


10.  If  the  distance  of  a  star  were  increased  by  40  per  cent,  how  much 
would  its  magnitude  be  changed? 

Ans.    0.73  of  a  magnitude,  numerical  increase. 

11.  If  the  distance  of  a  star  were  diminished  by  40  per  cent,  how 
would  its  magnitude  be  affected? 

Ans.    1.11  magnitude,  numerical  decrease. 

12.  If  a  star  of  the  ninth  magnitude  has  a  parallax  of  0".25,  how  does 
the  light  emitted  by  it  compare  with  that  of  the  sun?  AnSt      i 


Paris  Observatory,  from  the  Garden 


CHAPTER  XX 
STELLAR   SYSTEMS,  CLUSTERS,  AND   NEBULJE 

Double  and  Multiple  Stars  —  Binaries  —  Spectroscopic  Binaries  —  Clusters  —  Nebulae 
—  The  Stellar  Universe  —  Cosmogony 

585.  Double  Stars.  —  The  telescope  shows  numerous  cases  in 
which  two  stars  lie  so  near  each  other  that  they  can  be  sepa- 
rated only  by  a  high  magnifying  power.  These  are  double  stars,  Double 

stars. 


FIG.  190.  —  Double  and  Multiple  Stars 

and  at  present  nearly  fifteen  thousand  such  couples  are  known. 
There  is  also  a  considerable  number  of  triple  stars  and  a  few  Triple  and 
are  quadruple.     Fig.  190  represents  some  of  the  best  known  multlPle 
telescopic  objects  of  each  class. 

537 


538 


MANUAL   OF   ASTRONOMY 


Apparent 
distances. 


Color. 


Distance 
and  position 
angle. 


Optical  and 

physical 

doubles. 


The  apparent  distances  generally  range  from  30"  downwards, 
very  few  telescopes  being  able  to  separate  stars  closer  than  one 
fourth  of  a  second.  In  a  large  proportion  of  cases,  perhaps  one 
third  of  all,  the  two  components  are  nearly  equal;  in  many, 
however,  they  are  very  unequal :  in  that  case  (never  when  they 
are  equal)  they  often  present  a  contrast  of  color,  and  when  they 
do  the  smaller  star,  for  some  reason  not  yet  known,  almost 
without  exception,  has  a  tint  higher  in  the  spectrum  than  that 

of  the  larger,  —  if  the 
larger  star  is  reddish  or 
yellow,  the  smaller  is 
green,  blue,  or  purple. 
7  Andromedse  and 
ft  Cygni  are  fine  ex- 
amples for  a  small  tele- 
scope. 

The  distance  and  posi- 
tion angle  of  a  double 
star  are  usually  meas- 
ured with  the  filar  mi- 
crometer, the  position 
angle  being  the  angle 

FIG.  191. -Measurement  of  Distance  and  Position     made   at  the  laJBer  stal> 

Angle  of  a  Double  Star  between  the  north  and 

south  line  and  the  line 

which  joins  the  stars.  This  angle  is  always  reckoned  from  the 
north  through  the  east,  completely  around  the  circle;  i.e.,  if 
the  smaller  star  were  southeast  of  the  larger  one,  its  position 
angle  would  be  135°.  Fig.  191  illustrates  the  matter.  The 
position  angle  of  the  double  star  shown  is  about  325°. 

586.  Stars  optically  and  physically  Double.  —  Stars  may  be 
double  in  two  ways,  —  optically  or  physically.  In  the  first  case 
they  are  one  far  beyond  the  other,  but  nearly  in  line  as  seen  from 
the  earth.  In  the  second  case  they  are  really  near  each  other. 


STELLAR  SYSTEMS,  CLUSTERS,  AND  NEBULAE   539 

In  the  case  of  stars  that  are  only  optically  double  it  usually  Criterion  by 
happens  that  we  can,  after  some  years,  detect  their  mutual  inde-  whlch  ihw 

may  be  dis- 

pendence  by  the  fact  that  their  relative  motion  is  in  a  straight  tinguished. 
line  and  uniform.     This  is  a  simple  consequence  of  the  combi- 
nation of  their  independent  rectilinear  proper  motions. 

If  they  are  physically  connected,  we  find,  on  the  contrary,  that 
the  relative  motion  is  not  in  a  straight  line,  but  in  a  concave 
curve;  i.e.,  taking  one  of  the  two  as  a  center,  the  other  moves 
around  it. 

The  doctrine  of  chances  shows,  what  direct  observation  con- 
firms, that  the  optical  pairs  must  be  comparatively  rare  and  that  Optical 
the  great  majority  of  double  stars  must  be  physically  connected, 
—  in  all  probability  by  the  same  attraction  of  gravitation  which 
controls  the  solar  system. 

587.  Binary  Stars.  —  Stars  thus  physically  connected  are 
known  as  "  binary."  They  revolve  in  elliptical  orbits  around 
their  ccmmon  center  of  gravity  in  periods  which  range  from 
eleven  to  fifteen  hundred  years  (so  far  as  at  present  known), 
while  the  apparent  major  axis  of  the  oval  ranges  from  40" 
to  0".3. 

Sir  William  Herschel,  a  little  more  than  a  century  ago,  first  Discovery  of 
discovered  this  orbital  motion  in  trying  to  ascertain  the  parallax  bmary  stars 
of  some  of  the  few  double  stars  that  were  known  at  his  time.  Herschel. 
It  was  then  supposed  that  they  were  simply  optical  pairs,  and 
he  expected  to  find  an  annual  parallactic  displacement  of  one  of 
the  stars  with  reference  to  the  other.     He  failed  in  this,  but 
found  instead  a  true  orbital  motion. 

At  present  the  number  of  pairs  in  which  this  orbital  motion 
has  been  certainly  detected  is  over  two  hundred  and  is  rapidly 
increasing  with  time.  Most  of  the  double  stars  have  been  dis- 
covered too  recently  to  show  much  motion  as  yet,  but  about 
fifty  pairs  have  progressed  so  far — either  having  completed  an 
entire  revolution  or  a  large  part  of  one — that  it  is  possible  to 
compute  their  orbits  with  some  precision. 


540 


MANUAL   OF   ASTRONOMY 


Their  orbits. 


Determina- 
tion of  the 
true  orbit 
from  the 
apparent. 


Micrometer 
observations 
give  only 
the  relative 
orbit. 


7  Virginia 


f  UrsceMajorts 


588,  Orbits  of  Binaries. — In  the  case  of  a  binary  pair  the  appar- 
ent orbit  of  the  smaller  star  with  reference  to  the  larger  one  is 
always  an  ellipse ;  but  this  apparent  orbit  is  only  the  true  orbit 
seen  more  or  less  obliquely,  and  the  larger  star  is  usually  not 
in  its  focus.    If  we  assume  what  is  probable,1  though  not  proved 
as  yet,  that  the  orbital  motion  of  the  pair  is  under  the  law  of 
gravitation,  we  know  that  the  larger  star  must  be  in  the  focus 
of  the  true  relative  orbit  described  by  the  smaller,  and,  more- 
over, that  the  latter  must  de- 
scribe around  it  equal  areas 
in  equal  times.    By  the  help 
of  these  principles  it  is  pos- 
sible to  deduce  from  the  ap- 
parent oval  the  true  orbital 
ellipse ;  but  the  calculation 
is  troublesome  and  delicate, 
and  the  result  in  most  cases 
is  to  be  regarded  as  at  pres- 
ent   only    approximate,    on 
account  of  the  insufficiency 
of  data. 

Fig.  192   represents   the 
orbits  of  three  of  the  best 

FIG.  192.  —  Binary  Systems :  Apparent  Orbits      ,    .          .        ,  r^, 

determined    systems.      The 

fourth,  that  of  61  Cygni,  is  still  very  uncertain,  and  the  motion 
indicated  in  the  diagram  is  very  doubtful. 

589,  Orbit  of  Sirius.  —  The  relative  orbit  is  all  that  can  be 
determined  from  micrometer  observations  of  the  distance  and 
position  angle  between  the  two  stars  of  a  binary  pair ;  but  in  a 
few  cases,  where  we  have  sufficient  meridian-circle  observations, 

lrThe  question  can  be  decided  by  spectroscopic  observations  whenever  we 
become  able  to  observe  separately  the  two  spectra  of  the  components  of  a  binary 
and  so  can  determine  the  radial  velocity  of  each  at  several  different  points  in 
the  orbit.  The  difficulties  of  observation  are  great,  but  probably  will  ulti- 
mately be  overcome. 


500  ±  Years 


58  Years 


180° 


-90° 


0° 
61  Cygni 


STELLAR   SYSTEMS,   CLUSTERS,    AND   NEBULA       541 

or  where  the  two  components  of  the  pair  have  had  their  position 
and  distance  separately  measured  from  neighboring  stars  not 
partaking  of  their  motion,  we  can  deduce  the  absolute  motion  of 
each  of  the  two  with  respect  to  their  common  center  of  gravity, 
and  thus  get  data  for  determining  their  relative  masses. 

The  case  of  Sirius  is  in  point.     Before  1850  Bessel,  from  Orbit  of 
meridian-circle  observations,  had  found  it  to  be  moving,  for  no 
(then)  assignable  reason,  in  a  small  oval  orbit  with  a  period 
of  about  fifty  years.     In  1862  Clark  found  near  it  a  minute 


FIG.  193.  —  Orbits  of  Sirius  and  its  Companion 

companion,  which  explained  everything ;  only  we  have  to  admit 
that  this  faint  acolyte,  which  does  not  give  y^^o"  Par^  as  mucn 
light  as  Sirius  itself,  has  a  mass  more  than  a  quarter  as  great ;  it 
was  the  first  discovery  of  one  of  Bessel's  "  dark  stars." 

Fig.  193  shows  the  absolute  and  relative  orbits  of  the  system  The  relative 
of  Sirius.     The  smallest  oval  is  the  orbit  of  Sirius  itself  as  orbitand 
determined  by  the  meridian-circle,  and  the  other  full-line  oval  real  orbits, 
is  the  actual  orbit  of  the  faint  companion  around  the  common 
center  of  gravity,  (7,  of  the  two  stars.      The  large  broken-line 
ellipse  is  the  relative  orbit  of  the  companion  with  respect  to 


542 


MANUAL   OF   ASTRONOMY 


Size  of 
binary 
orbits  com- 
parable with 
the  larger 
planetary 
o»bits. 


Sirius,  as  determined  by  micrometer  measures  of  distance  and 
position  angle.  When  the  small  star  is  at  B'  and  Sirius  itself 
at  A'  in  their  actual  orbits,  the  smaller  star  will  be  at  B"  in  the 
relative  orbit,  A"Bn  being  always  parallel  and  equal  to  A'B1. 

The  case  of  Procyon  is  similar,  but  its  period  is  not  yet 
determined. 

590.  Size  of  the  Orbits — The  real  dimensions  of  a  double- 
star  orbit  can  be  obtained  only  when  we  know  its  distance  from 
us.  Fortunately,  a  number  of  the  stars  whose  parallaxes  have 
been  ascertained  are  also  binary,  and  assuming  the  best  avail- 
able data  as  to  parallax  and  orbit,  we  find  the  following  results, 
— the  semi-major  axis  in  astronomical  units  being  always  equal 

a" 
to  the  fraction  — ,  in  which  a"  is  the  semi-major  axis  of  the 

double-star  orbit,  and  p"  its  parallax,  both  in  seconds  of  arc. 


NAME 

ASSUMED 
PARALLAX 

ANGULAR 

SEMI-AXIS 

REAL 

SEMI-AXIS 

PERIOD 
IN  YEARS 

MASS 

0  =  1 

17  Cassiopeise     .     > 

0".35 

8".  21 

23.5 

195.8 

0.33 

Sirius  

0  .39 

8  .03 

20.6 

52.2 

3.24 

o  Centauri   .     .     . 

0  .75 

17  .70 

23.6 

81.1 

2.00 

70  Ophiuchi      .     . 

0  .25(?) 

4  .55(?) 

18.2  (?) 

88.4 

0.77  (?) 

N.B.  —  The  parallaxes  here  assumed  differ  more  or  less  from  those  adopted 
by  Kapteyn  and  given  in  Table  IV  of  the  Appendix. 

These  double-star  orbits  are  evidently  comparable  in  magni- 
tude with  the  larger  orbits  of  the  planetary  system,  none  of 
those  given  being  smaller  than  the  orbit  of  Uranus  and  none 
quite  as  large  as  that  of  Neptune.  The  elements  of  the  orbits 
are  from  the  data  of  Dr.  See,  given  in  Table  VII  of  the  Appen- 
dix. In  the  case  of  Sirius  the  observations  made  since  the 
reappearance  of  the  companion  in  1897  indicate  that  the  true 
period,  distance,  and  mass  are  all  a  little  less  than  here  given. 
Spectroscopic  591.  Spectroscopic  Binaries.  —  One  of  the  most  interesting 
results  of  Spectroscopic  work  is  the  discovery,  dating  from  1889, 


binaries. 


STELLAR   SYSTEMS,    CLUSTERS,   AND   NEBULAE       543 

of  numerous  pairs  of  double  stars  so  close  that  no  telescope  can 
separate  them,  but  proved  to  be  double  by  the  behavior  of  the 
lines  in  their  spectra.  From  a  spectroscopic  point  of  view  these 
fall  into  two  classes : 

(a)  Those  in  which  the   duplicity  is  exhibited  by  a  back-  Those 
ward  and  forward  periodical  shift  of  the  lines  in  their  spectra,  fh{"*acter- 
as  observed  with  an  ordinary  spectroscope  with  slit  and  col-  shift  of 
limator,  but  not  observable  with  the  slitless  spectroscope.     In  8Pectrum 
cases   of  this  kind  only  one  of  the  stars  is  large   or  bright 
enough  to  show  an  observable  spectrum,  the  other  being  very 
faint. 

(6)  Those  which  not  only  shift  their  lines  but  also  periodi-  Those  in 
cally  double  and  undouble  them,  —  a  phenomenon  observable  with  whlch  lmes 

J  double  and 

the  slitless  spectroscope  as  well  as  with  an  instrument  of  the  undouble. 
more  usual  form.     In  this  case  the  two  stars  are  of  not  very 
unequal  brightness. 

592.   Spectroscopic  Binaries  of  the  First  Class.  — Algol,  already  Binaries  of 
described  (Sec.  582),  belongs  to  this  class,  and  Vogel  in  1889,  thefirst 
while  he  was  at  work  upon  this  star,  found  that  the  star  Spica 
(a  Virginis)  also  shifts  its  spectrum  lines  in  the  same  way,  in  a 
period  of  4d19m,  but  without  any  observable  variation  in  its 
brightness.     From  this  he  concluded  that  Spica  also  is  double, 
having  a  faint  or  dark  companion  like  Algol's,  but  with  the 
orbital  plane  so  much  inclined  that  the  bright  star  is  never 
eclipsed ;  the  smaller  one  never  comes  exactly  between  us  and 
the  larger  so  as  to  eclipse  it. 

From  the  amount  by  which  the  lines  shift,  Vogel,  assuming  Case  of 
the  orbital  inclination  to  be  small,  computes  that  Spica  moves  sPica  . 
in  an  orbit  about  13  000000  miles  in  diameter,  with  a  velocity  of 
about  56£  miles  a  second.     If,  however,  the  inclination  is  really 
considerable,  the  actual  orbital  velocity  must  be  much  higher 
and  the  orbit  larger.     As  to  the  velocity  of  the  smaller  star  in 
its  orbit,  we  have  no  data  (but  see  exercises  at  the  end  of  the 
chapter). 


544 


MANUAL   OF   ASTRONOMY 


More  recently  Belopolsky  of  Pulkowa,  Duner,  Sir  Norman 
Lockyer,  Newall,  and  others  in  Europe,  and  in  this  country 
Keeler  and  Campbell  especially,  at  the  Lick  Observatory,  have 
detected  a  considerable  number  of  other  binaries  of  this  class, 
among  which  the  most  notable  perhaps  are  the  following :  Cas- 
tor, 8  Cephei  (its  period  of  revolution  being  identical  with  that 
of  its  variability),  Capella,  with  a  long  period  of  104  days,  and 
Polaris,  which  latter,  like  Spica,  has  a  period  of  only  four  days 
and  an  extremely  low  range  of  apparent  radial  velocity,  prob- 
ably indicating  that  its  orbit  is  nearly  perpendicular  to  the  line 
of  sight. 

There  are  also  indications  that  Polaris  and  its  companion  are  together 
in  orbital  motion  around  a  much  more  distant  invisible  body  in  a  period, 
not  yet  deterininable,  of  many  years.  In  1889  the  star's  radial  velocity 
towards  the  earth  was  about  16  miles  a  second  ;  this  had  dropped  to  10  miles 
in  1896,  and  to  a  little  over  7  in  1899,  but  in  July,  1901,  it  had  increased 
to  8^,  having  apparently  reversed  its  tendency. 

Campbell  finds  that  about  one  in  six  of  all  the  stars  he  has 
thus  far  examined  shows  indications  of  similar  orbital  motion, 
and  is  now  engaged  in  an  extensive  campaign  for  studying  the 
motions  of  the  smaller  stars. 

In  the  case  of  /3  Lyrse  the  lines  of  its  spectrum  double  as  well 
as  shift. 

593.  Spectroscopic  Binaries  of  the  Second  Class.  —  In  1889, 
almost  simultaneously  with  Vogel's  discoveries  relating  to  Algol 
and  a  Virginis,  Professor  Pickering  announced  that  the  lines 
in  the  spectrum  of  the  brighter  component  of  the  well-known 
double  star  Mizar  (f  Ursse  Majoris),  as  photographed  in  the  slit- 
less  spectroscope,  double  themselves  at  regular  intervals  of  about 
fifty-two  days.  At  these  times  the  two  components,  not  very 
unequal  in  brightness,  are  moving  one  towards,  the  other  from, 
us,  their  relative  velocity  being  about  100  miles  a  second.  From 
all  the  observations  then  available  he  concluded  that  the  orbit 
was  an  eccentric  ellipse  described  in  a  period  of  104  days,  with 


STELLAR   SYSTEMS,   CLUSTERS,   AND   NEBULA       545 

a  semi-major  axis  of  about  140  000000  miles;  but  certain 
irregularities  in  the  observations  made  some  of  his  conclusions 
doubtful. 

Vogel,  in  a  paper  published  in  1901,  announced  recent  photo-  Vogei'scor- 
graphic  observations  of  the  spectrum  of  the  star  made  with  the  p^ering's 
newly  erected  instrument  figured  in  our  frontispiece,  which,  result  as  to 
while  substantially  confirming  the  relative  velocity  observed  by  ^"of  orMt 
Pickering,  give  a  period  of  only  20.6  days, — just  one  fifth  of 
Pickering's  period. 

Assuming  the  orbit  to  be  circular  and  its  inclination  small, 
this  corresponds  to  a  semi-major  axis  of  about  28  330000  miles 
and  a  mass  nearly  nine  times  that  of  the  sun. 

The  lines  in  the  spectrum  of  J3  Aurigae  present  the  same  peculiarity,   /s  Aurigae : 
but  the  doubling  occurs  once  every  two  days,  and  the  relative  velocity  of  velocity  150 

the  pair  is  150  miles  a  second ;  the  diameter  of  the  orbit  appears  to  be   miles  a 

second 

about  16  500000  miles,  and  the  united  mass  of  the  pair  about  Jive  and  one- 
half  times  that  of  the  sun. 

The  two  most  remarkable  objects  of  this  class  were  discovered  in  1896   ^  Scorpii: 
by  spectrum  photographs  made  at  Arequipa.     The  first  is  /x1  Scorpii  (fourth   velocity  30° 
magnitude),  in  which  the  relative  velocity  of  the  components  is  nearly 
300  miles  a  second  and  the  period  34h42m.5.     This  makes  the  diameter  of 
the  relative  orbit,  if  circular,  about  6  050000  miles  and  the  mass  of  the 
system  about  eighteen  times  that  of  the  sun. 

The  other  is  a  little  star  of  the  fifth  magnitude,  known   as  Lacaille   Lacaille 
3105.     The  relative  velocity  of  this  pair  is  no  less  than  385  miles  a  second  3105: 
and  the  period  74h46m,  corresponding  to  an  orbital  diameter  of  16  500-  ve.locity  385 
000  miles  and  a  mass  seventy-seven  times  that  of  the  sun. 

About  300  spectroscopic  binaries  were  known  in  1910,  and  About  300 
the  number  is  fast  increasing.  The  majority  belong  to  the  first  class.  fPectros( 

594.  Masses  of  Binary  Systems.  —  If  we   assume  that  the  known, 
binary  stars  move  under  the  law  of  gravitation,  then,  when  we 
have  ascertained  the  semi-major  axis  of  the  real  orbit  in  astro- 
nomical units  and  the  period  of  revolution  in  years,  we  can  at 
once  find  the  mass  of  the  pair  as  compared  with  that  of  the  sun 


546 


MANUAL   OF   ASTRONOM1 


by  the  proportion  from  Sec.  380,  in  which  the  third  term  becomes 
unity  when  the  distance  and  period  are  expressed  as  stated, 


Formula  for 
mass  of  a 
binary 
system. 
Results 
liable  to  a 
large  error. 


Density  of 
spectro- 
scopic 
binaries 
very  low. 


Results  of 
Russell  for 
limits  of 
density. 


Evolution 
of  binary 
systems. 


.. 

In  this  proportion  (S  +  e)  is  the  united  mass  of  the  sun  and 
earth,  e  being  insignificant,  while  (M  -+-  m)  is  the  united  mass  of 
the  two  stars.  This  gives 

S~ 

The  final  column  of  the  little  table  of  Sec.  590  gives  the  masses  of  the 
star  pairs  resulting  from  the  data  there  presented  ;  but  the  reader  must 
bear  in  mind  that  they  are  liable  to  large  error  because  of  the  uncertainty 
of  the  parallaxes,  —  a  slight  error  in  the  parallax  produces  a  vastly  greater 
error  in  the  computed  mass. 

The  reader  is  also  again  reminded  of  the  fact  that  the  mass  of  a  pair 
gives  no  clue  to  the  diameter  or  density  of  the  stars  ;  though  what  has  been 
ascertained  in  the  case  of  Algol  and  other  stars  of  the  same  class  of  vari- 
able indicates  that  generally  their  densities  are  small  compared  with  that 
of  the  sun.  Russell  of  Princeton  and  Roberts  of  South  Africa  have  recently 
shown,  simultaneously  and  independently,  that  in  the  case  of  the  Algol  vari- 
ables it  is  possible  from  the  period,  the  duration  of  obscuration,  and  the 
peculiarities  of  the  light  curve  during  the  "  eclipse  "  to  determine  the  maxi- 
mum value  possible  for  the  mean  density  of  the  system.  From  eight  or 
ten  of  these  variables  —  all  for  which  observation  furnishes  the  necessary 
data  —  Russell  found  values  of  the  limiting  density  in  terms  of  that  of 
water,  ranging  from  0.035  in  the  case  of  S  Cancri  to  0.728  for  Z  Herculis. 
The  density  of  the  sun  is  1.41. 

595.  Evolution  of  Binary  Systems.  —  As  already  remarked, 
the  theory  of  probabilities  indicates  that  the  great  majority  of 
double  stars  must  be  physically  connected,  but  our  observations 
have  not  yet  continued  long  enough  to  give  us  any  accurate 
knowledge  of  the  orbits  of  more  than  a  very  few.  Table  VII 
(Appendix)  presents  a  list  of  twenty,  mostly  computed  by 
Dr.  See,  which  may  be  regarded  as  fairly  known.  Two  others 
of  long  period  are  added,  not  yet,  however,  to  be  accepted  as 
trustworthy,  the  data  being  still  insufficient. 


STELLAR   SYSTEMS,   CLUSTERS,   AND   NEBULAE       547 

It  will  be  noticed  that  these  orbits  are  very  eccentric  as  com-  Eccentricity 
pared  with  those  of  the  planets,  their  average  eccentricity  being  of  sftellar 
nearly  0.50.     Dr.  See  has  investigated  the  probable  origin  of  large, 
these  binary  systems  and  finds  that  the  peculiarities  of  their 
orbits  can  be  accounted  for  by  the  theory  of  "tidal  evolution."  Peculiarities 
It  is  supposed  that  in  such  cases  the  primitive  nebula  in  whirl-  exPlamed 

by  tidal 

ing  assumed  the  dumb-bell  form  known  as  the  "apioid";  that  evolution, 
the  two  parts  then  separated  into  a  spectroscopic  double,  and  as 
they  revolved  around  their  common  center  of  gravity  great  tides 
were  raised  upon  them,  which,  as  mathematically  proved,  must 
tend  to  push  the  spinning  globes  apart  into  eccentric  orbits. 
(See  Sec.  346.) 

596,  Planetary   Systems    attending  Stars.  —  It  is  a  natural  Question 
question  whether  some,  at  least,  of  the  stars  have  not  planetary  of  Planets 

attending 

systems  of  their  own,  and  whether  some  of  the  small  "compan-  stars. 
ions"  that  we  see  may  not  be  the  Jupiters  of  such  systems. 

While  it  is  entirely  possible  that  many  of  the  stars  do  have 
such  attendant  planets,  we  can  only  say  that  no  telescope  ever 
yet  constructed  could  even  come  near  to  making  visible  a  planet  invisible  if 
bearing  to  its  primary  the  relations  of  size,  distance,  and  bright-  they  exist* 
ness  which  Jupiter  bears  to  the  sun. 

As  viewed  from  our  nearest  neighbor  among  the  stars,  Jupiter  would 
be  a  star  of  about  the  twenty-first  magnitude  and  not  quite  5"  distant 
from  the  sun,  which  itself  would  be  a  star  of  the  second  magnitude.  To 
render  a  star  of  the  twenty-first  magnitude  barely  visible  (apart  from  all 
the  difficulties  raised  by  the  nearness  of  an  immensely  brighter  star)  would 
require  a  telescope  of  more  than  20  feet  in  diameter. 

597.  Multiple  Stars There  are  a  considerable  number  of  Multiple 

cases  where  we  find  three  or  more  stars  connected  in  a  single  stars' triple 

and  quad- 
System,      f  Cancri  (Figs.  190  and  192)  consists  of  a  close  pair  rupie. 

revolving  in  a  nearly  circular  orbit,  with  a  period  of  somewhat 
less  than  sixty  years,  while  a  third  star  revolves  in  the  same 
direction  around  them  at  a  much  greater  distance  and  with  a 
period  that  must  be  at  least  five  hundred  years.  Moreover,  the 


548 


MANUAL   OF   ASTRONOMY 


Asterope  • 


third  star  appears  to  be  subject  to  a  peculiar  irregularity  in  its 
motion,  which  seems  to  indicate  that  it  has  near  it  a  companion 
unseen  as  yet,  the  system  probably  being  really  quadruple. 

In  e  Lyrse  we  have  a 
most  beautiful  quadruple 
system,  composed  of  two 
pairs,  each  pair  making 
its  own  slow  revolution 
with  a  period  not  yet 
determined,  but  probably 
exceeding  two  hundred 
years ;  moreover,  since 
they  have  an  identical 
proper  motion,  the  two 
pairs  probably  revolve 
around  each  other  in  a 
period  to  be  reckoned 
only  by  thousands  of 
years. 


Pleione* 
Atlast 


Alcyone  J, 


• 
Celceno 


Electro 


FIG.  194.  —  Map  of  the  Pleiades 


In  6  Orionis  we  have  a  multiple  star  in  which  the  six  com- 
ponents are  not  arranged  in  pairs,  but  are  at  not  very  unequal 
distances  from  each  other  (Fig.  190). 


Star- 
clusters. 


Naked-eye 
groups. 


STAK-CLUSTEBS 

598.  There  are  in  the  sky  numerous  groups  of  stars,  con- 
taining from  a  hundred  to  many  thousand  members.  A  few 
are  resolvable  by  the  naked  eye,  as,  for  instance,  the  Pleiades 
(Fig.  194);  some,  like  "Praesepe"  (in  Cancer),  break  up  under 
the  power  of  even  an  opera-glass ;  but  most  of  them  require 
a  large  telescope  to  show  the  separate  stars.  To  the  naked  eye 
or  small  telescopes,  if  visible  at  all,  they  look  merely  like  faint 
globular  clouds  of  shining  haze,  but  in  a  large  instrument  they 
are  among  the  most  magnificent  objects  the  heavens  afford. 


STELLAR   SYSTEMS,   CLUSTERS,   AND   NEBULAE       549 


The  cluster  known  as  "13  Messier"  (Herculis),  not  far  from 
the  "apex  of  the  sun's  way,"  is  the  finest  in  the  northern 
heavens,  containing  several  thousand  stars  within  a  space  one 
fourth  of  the  diameter  of  the  moon.  o>  Centauri,  in  the  south- 
ern hemisphere,  is  perhaps  even  finer.  (See  Fig.  195,  from  an 
Arequipa  photograph.) 

The  question  at  once  arises  whether  the  stars  in  such  a  cluster 
are  comparable  with  our  own  sun  hi  magnitude  and  separated 
from  each  other  by  distances  like  that  between  the  sun  and 
a  Centauri,  or  whether  they  are  really  small  and  closely 
packed,  —  mere  sparks  of  stellar  matter;  whether  the  swarm 
is  about  the  same  distance  from  us  as  the  stars  or  far  beyond 
them. 

Half  a  century  ago  the  prevalent  view  was  that  they  and  the 
nebulae  (the  nebulae  being  then  supposed  to  be  really  clusters) 
are,  in  fact,  "stellar 
universes"  so  remote 
that  the  separate  stars 
can  be  made  out  only 
with  the  telescope,— 
"Galaxies,"  like  the 
group  of  stars  to  which 
it  was  supposed  the 
sun  belongs,  but  so 
inconceivably  distant 
that  in  appearance  they 
dwindle  to  mere  shreds 
of  luminous  cloud.  It 
is  now,  however,  quite 
certain  that  the  oppo- 
site view  is  correct. 
These  objects  are 
among  our  stars  and  form  a  part  of  our  own  stellar  universe. 
Large  and  small  stars  are  so  associated  in  the  same  clusters 


Telescopic 
clusters. 


FIG.  195.  — Cluster  of  u  Centauri 


Stars  in 
telescopic 
clusters 
probably 
really  small. 


Star-clusters 
belong  to 
our  stellar 
system : 
not  remote 
Galaxies. 


550 


MANUAL   OF   ASTRONOMY 


and  nebulae  (see  Fig.  196)  as  to  leave  no  doubt  on  the  point, 
although  it  has  never  yet  been  possible  to  determine  the  actual 
parallax  and  distance  of  any  cluster.  or  nebula. 


The  nebulae, 


The  larger 


irregular 
inform. 


Their 


Smaller 
nebulae 

mostly  oval 

with  brighter 
center. 

Pianetary 


NEBULA 

599.  Besides  the  clusters  there  are  other  luminous  clouds 
which  no  telescopic  power  resolves  into  stars,  and  among  them 
some  which  are  brighter  than  many  of  the  clusters.  These  irre- 
solvable  objects  are  the  nebulce  (clouds),  of  which  something  like 
ten  thousand  are  now  catalogued,  with  probably  hundreds  of 
thousands  as  yet  uncatalogued,  but  discoverable  by  photography. 
Half  a  dozen  of  them  are  visible  to  the  naked  eye,  —  one,  the 
brightest  of  all  and  the  one  in  which  the  temporary  star  of 
1885  appeared,  is  the  Great  Nebula  of  Andromeda  (Fig.  200). 
Another,  next  in  brightness  and  the  most  beautiful  nebula  of 
^  ig  ^  ^  ^  SWQrd  of  Orion.  (See  Fig.  197,  from  Keeler's 
magnificent  photograph  of  the  nebula,  made  in  1900.) 

The  larger  and  brighter  nebulae  are  mostly  irregular  in  form, 
sending  out  sprays  and  streams  in  all  directions  and  containing 
dark  openings  and  "lanes."  They  are  of  enormous  volume. 
The  nebula  of  Orion  (which  includes  within  itself  the  multiple 
star  0  Orionis)  covers  several  square  degrees,  and  since  we  know 
with  certainty  that  it  is  far  more  remote  than  a  Centauri,  its 
cross-section  as  seen  from  the  earth  must  exceed  the  area  of  Nep- 
tune's  or^t  ^v  many  thousand  times.  The  nebula  of  Andromeda 
fe&ftt  quite  so  extensive,  and  it  is  rather  more  regular  in  form, 
tfiough  it  shows  curious  dark  streaks  within  it. 
|  The  smaller  nebulae  are  usually  more  or  less  nearly  oval  and 
brighter  in  the  center.  In  the  so-called  nebulous  stars  the  central 

^  . 

nucleus  looks  like  a  star  shining  through  a  fog. 

The  planetary  nebulae  are  nearly  circular  and  of  about  uni- 
form  brightness  throughout,  and  the  rare  annular  or  ring 
ne^ulcB  are  darker  in  the  center;  the  finest  of  these  is  the  one 


FIG.  196.  —  Pleiades  and  Enveloping  Nebulae 
Roberts 


FIG.  197.  — Great  Nebula  of  Orion 
Keeler 


FIG.  198.  —  Annular  Nebula  in  Lyra 
Keeler 


FIG.  199.  —  The  Whirlpool  Nebula 
Keeler 


552 


MANUAL   OF   ASTRONOMY 


r*fe 


Spiral 
nebulae 


Drawings 
and  engrav- 


in  the  constellation  of  Lyra  (Fig.  198).  Many  of  the  nebulae 
exhibit  a  'remarkable  ,$piral  or  whirlpool-like  structure  in  large 
telescopes  ;">  Indeed,  the  photographic  work:  of  Keeler  shows  , 
thatvthis.  spiral,  structure  is  perhaps  predominant  in  the  great 
majority  of  nebulae.  Fig.:  199  is  from  his '  photograph  of  the 
.  \<  whirlpool  nebula,"  51  Messier.  There  are  numerous 


FIG.  200.  —  Nebula  of  Andromeda 
Roberts 


double  nebulae,  perhaps  double  stars  in  process  of  making,  and  a 
few  that  are  variable  in  brightness,  though  no  periodicity  has 
yet  been  ascertained  in  their  variations. 

The  great  majority  of  the  nebulae  are  extremely  faint,  but  the 
few  that  are.  reasonably  bright  are  very  interesting  objects  with 
large  telescopes. 

600,  Drawings  and  Photographs  of  Nebulae.  —  Not  very  long 
agQ  tke  Correct  representation  of  a  nebula  was  an  extremely 
difficult  task.  A  few  more  or  less  elaborate  engravings  exist 


STELLAR   SYSTEMS,   CLUSTERS,    AND   NEBULAE       553 

of  perhaps  fifty  of  the  most  conspicuous,  but  photography  has 
recently  taken  possession  of  the  field.  The  first  success  in  this 
line  was  by  Henry  Draper  of  New  York,  in  1880,  in  photo- 
graphing the  nebula  of  Orion. 

Since  his  death  in  1882  great  progress  has  been  made,  both  Superseded 
in  Europe  and  this  country,  and  at  present  photographs  have  byPhot°- 
quite  superseded  drawings.     The  photographs  are  continually  which  reveal 
bringing  out  new  and  before  unsuspected  features  not  visible  in  features 

not  visible 

any  telescope.    Fig.  200,  for  instance,  is  a  half-tone  reproduction  jn  telescope. 


FIG.  201.  —  Great  Nebula  in  Monoceros 
__  Roberts 

of  a  photograph  of  the  nebula  of  Andromeda,  taken  by  Mr. 
Roberts  of  Liverpool  in  1888,  which  was  a  revelation  to  astrono- 
mers. It  shows  that  the  so-called  "dark  lanes,"  which  up  to 
that  time  had  been  seen  only  as  straight  and  wholly  inexplicable 
markings,  are  really  curved  ovals,  like  the  divisions  in  Saturn's 
rings,  and  brings  out  clearly  a  distinct  annular  or  spiral  structure 
pervading  the  whole  nebula,  though  never  yet  seen  by  the  eye. 

Fig.  201  is  a  photograph  by  Roberts  of  a  faint  but  enormous 
nebula  which  covers  an  area  more  than  a  degree  in  diameter 


554  MANUAL   OF   ASTRONOMY 

in  the  constellation  of  Monoceros,  —  apparently  a  chaos  in  the 
initial  stages  of  evolution. 

Certain  dis-  The  photograph  has  its  drawbacks,  however  ;  stars  present  in 
advantages  ^Q  nebulae  are  not  properly  shown,  nor  is  the  relative  brightness 
raphy.  of  different  portions  fairly  given  on  any  single  negative.  The 

exposure  necessary  to  bring  out  faint  details  is  far  too  great  for 
the  brighter  parts  of  the  nebula  and  wholly  destroys  the  stars. 
Moreover,  the  nebula  is  very  rich  in  ultra-violet  light,  so  that 
the  relative  photographic  brightness  of  different  parts  differs 
from  the  visual.  In  Fig.  203  (Sec.  602),  made  with  a  slitless 
spectroscope  used  as  a  "  prismatic  camera,"  the  brightest  images 
of  the  annular  nebula  in  Lyra  are  ultra-violet,  made  by  light 
invisible  to  the  eye. 

Photog-  The  photographs  not  only  show  new  features  in  old  nebulge, 

raphy  multi-  ^^  faoy  reveal  immense  numbers  of  nebulas  invisible  to  the  eye 
the  number  with  any  telescope.  Thus,  in  the  Pleiades,  it  has  been  found 


of  known  ^na^  near]y  all  the  larger  stars  have  wisps  of  nebulous  matter 
attached  to  them,  as  shown  by  Fig.  196,  from  a  photograph  by 
Roberts.  In  a  small  territory  in  and  near  the  constellation  of 
Orion,  Pickering,  with  an  8-inch  photographic  telescope,  found 
upon  his  negatives  nearly  as  large  a  number  of  new  nebulae  as 
those  that  were  previously  known  within  the  same  boundary, 
and  in  -1892  Wolf  of  Heidelberg  found  130  small  planetary 
nebulae  in  a  circle  of  1°  radius  around  the  star  rj  Virginis. 
Keeler  also  concluded  that  the  number  that  could  be  photo- 
graphed with  his  3-foot  reflector  must  be  "  many  times  greater  " 
than  those  that  could  be  seen  with  it. 

Very  recently  Wolf  has  begun  a  systematic  campaign  for  the 
purpose  of  discovering  and  cataloguing  objects  of  this  class, 
using  the  magnificent  twin  cameras  of  16-inch  aperture,  with 
lenses  made  by  Brashear,  provided  by  the  liberality  of  the  late 
Miss  Bruce. 

The  photographs  of  nebulas  require  generally  an  exposure  of 
from  one  to  four  or  five  hours,  or  even  more,  and  it  may  be 


STELLAR   SYSTEMS,   CLUSTERS,    AND   NEBULA       555 

noted  in  passing  that  thus  far  the  finest  nebular  photographs 
have  been  made  with  reflecting  telescopes. 

601.  Changes  in  Nebulae.  —  It  cannot,  perhaps,  be  stated  with  Question  of 
certainty  that  sensible  changes  have  occurred  in  any  of  the 
nebulae  since  they  first  began  to  be  observed,  — -the  early  instru- 
ments were  so  inferior  to  the  modern  ones  that  the  older  draw- 
ings cannot  be  trusted  very  far;  still,  some  of  the  differences 
between  them  and  more  recent  representations  and  photographs 

make  it  extremely  probable  that  real  changes  are  going  on. 

At  present  the  best  authenticated  instance  of  such  a  change,  according 
to  Professor  Holden,  is  in  the  so-called  "trifid"  nebula  in  Sagittarius. 
In  this  object  there  is  a  peculiar  three-armed  area  of  darkness  which 
divides  the  nebula  into  three  lobes.  A  bright  triple  star,  which  in  the 
early  part  of  the  century  was  described  and  figured  by  Herschel  and  other 
observers  as  in  the  middle  of  one  of  these  dark  lanes,  is  now  certainly  in 
the  edge  of  the  nebula  itself.  The  star  does  not  seem  to  have  moved  with 
reference  to  the  neighboring  stars,  and  it  seems,  therefore,  that  the  nebula 
itself  must  have  drifted  and  changed  its  form. 

602.  Spectra  of  Nebulae.  —  One  of  the  most  important  of  the  Spectrum 
early  achievements  of  the  spectroscope  was  the  proof  that  the  ^^ 
light  of  the  nebulae  proceeds  not  from   aggregations  of  stars,  Hugginsin 
but  from  glowing  gas  in  a  condition  of  no  great  density;  Sir  1864t 
William  Huggins,  in  1864,  first  made  the  decisive  observation 

by  finding  bright  lines  in  their  spectra. 

Thus  far  the  spectra  of  all  the  nebulae  that  show  lines  at  A  bright- 
all  appear  to  be  substantially  the  same.     Four  bright  lines  are 
usually  easily  observed :  two  of  them  are  due  to  hydrogen ;  but  trum. 
the  other  two,  in  the  bluish  green  (which  are  much  brighter  than 
the  hydrogen  lines),  are  not  yet  identified  and  are  almost  certainly 
due  to  some  element  not  yet  detected  on  the  earth  or  sun  and  Brightest 
apparently  peculiar  to  the  nebulce.  lines  due  to 

an  unknown 

At  one  time  the  brightest  of  the  four  lines  (X  5007)  was  thought  to  be  ^^ 
due  to  nitrogen,  and  even  yet  the  statement  is  found  in  some  books ;  but  hydrogen 
it  is  now  certain  that,  whatever  it  may  be,  nitrogen  is  not  the  substance,  and  helium, 


556 


MANUAL   OF   ASTRONOMY 


Mr.  Lockyer  later  ascribed  this  line  to  magnesium,  in  connection  with 
his  "meteoritic  hypothesis";  but  subsequent  observations  show  con- 
clusively that  this  identification  also  is  incorrect.  The  line  and  its 
neighbor  (A.  4959)  still  remain  a  mystery. 


Fig.   202   shows  the   position  of  the  principal  lines  so  far 
visually  observed ;  in  the  brighter  nebulae  a  number  of  others 


About 
seventy 
lines  have 

been  photo-    are  also  sometimes  seen  and  over  seventy  have  been  photographed 
-graphed.        jn  the  spectra  of  different  nebulae ;  the  lines  of  helium,  as  well 
as  hydrogen,  are  generally  found  to  be  present. 

Fig.  203  is  from  a  photograph  by  Gothard  of  the  ring  nebula 
and  a  number  of  planetary  nebulae  made  with  a  slitless  spectro- 
scope. In  this  case  each  bright  line  of  the  nebular  spectrum 


FIG.  202.  —  Visual  Spectrum  of  the  Gaseous  Nebulae 

is  replaced  by  an  image  of  the  object,  though  the  blue-violet 
and  ultra-violet  rays  alone  have  impressed  themselves  upon 
the  plate,  and,  as  already  mentioned,  the  brightest  photo- 
graphic image  of  the  ring  nebula  is  due  to  invisible  ultra-violet 
light. 

At  the  bottom  of  the  figure  is  the  photograph  of  Nova 
Aurigae,  made  in  the  same  way,  and  showing  the  identity  of 
the  spectrum  of  the  star  at  that  time  with  the  nebular  spec- 
trum. 

One  of  Huggins'  photographs  of  the  spectrum  of  the  nebula 
of  Orion  shows,  in  addition  to  the  bright  lines  that  are  visible 
to  the  eye,  a  considerable  number  in  the  ultra-violet ;  and  what 
is  interesting,  these  lines  seem  to  pertain  also  to  the  spectrum 
of  the  stars  in  the  so-called  "  Trapezium  "  (6  Orionis) ;  as  if,  which 


STELLAR   SYSTEMS,   CLUSTERS,   AND  NEBULA       557 

is  very  likely,  the  stars  themselves  were  mere  condensations  of 
the  nebulous  matter.  Indeed,  the  telescope  shows  that  close 
around  each  star  the  nebulous  matter  has  partially  disappeared, 
as  if  it  had  been  absorbed  by  it. 

Not  all  the  nebulae  show  the  bright-line  spectrum.     Those  Some 
which  do  —  about  half  the  whole  number  —  are  of  a  greenish  £  conthiuous 
tint,  at  once  recognizable  in  a  large  telescope.  spectrum. 

The  spiral  nebulae,  with  the  nebula  of  Andromeda,  the  bright- 
est of  all,  at  their  head,  present  a  continuous  background,  some- 
times crossed  by  faint  absorption  or  bright  lines.  This  does  not 


FIG.  203.  —  Nebulae  and  Nova  Aurigae 
Gothard 

necessarily  indicate  that  the  luminous  matter  is  not  gaseous, 
for  a  gas  under  pressure  gives  a  continuous  spectrum,  like  an 
incandescent  solid  or  liquid. 

The  telescopic  evidence  as  to  the  non-stellar  constitution  of 
nebulae  is  the  same  for  all;  no  nebula  resists  all  attempts  at 
resolution  more  stubbornly  than  that  of  Andromeda, 


558 


MANUAL   OF   ASTRONOMY 


Keeler,  at  the  Lick  Observatory,  with  a  powerful  spectroscope 
has  been  able  to  detect  and  to  measure  the  radial  motion  of 
several  of  the  brighter  nebulse.  It  appears  to  be  of  the  same 
order  as  that  of  the  stars,  the  nebulae  observed  giving  results 
ranging  from  0  up  to  about  40  miles  a  second, —  some  approach- 
ing and  others  receding. 

603.  Nature   of  the   Nebulae As  to  the  real  constitution 

and  temperature  of  these  bodies  we  can  only  speculate. 

The  fact  that  the  matter  which  shines  is  mainly  gaseous  does 
not  indicate  that  they  do  not  also  contain  dark  matter,  either 
liquid  or  solid,  nor  even  that  this  dark  matter  may  not  con- 
stitute the  main  portion  of  the  nebulous  mass.  In  the  green 
nebulse  we  can  say  with  confidence  that  hydrogen,  helium,  and 
some  unknown  gas  are  certainly  present,  and  that  these  gases 
emit  most  of  the  light  that  reaches  us  from  them.  But  how 
much  other  less  luminous  matter  in  the  form  of  grains  and 
drops  may  be  included  within  the  gaseous  cloud  we  cannot 
tell. 

The  idea  of  Mr.  Lockyer  (a  part  of  his  wide  induction  as  to 
what  may  be  called  the  "meteoritic  constitution  of  the  universe") 
is  that  they  are  clouds  of  "  sparse  meteorites,  the  collisions  of 
which  bring  about  a  rise  of  temperature  sufficient  to  render 
luminous  one  of  their  chief  constituents,1'  which  some  years  ago, 
when  the  sentence  was  written,  he  imagined  to  be  magnesium, 
though  that  is  no  longer  maintained. 

How  far  this  theory  will  stand  the  test  of  time  and  future 
investigations  remains  to  be  seen.  It  is  very  doubtful,  how- 
ever, whether  the  collisions  in  such  a  body  could  be  frequent  or 
violent  enough  to  account  for  its  luminosity,  and  one  is  tempted 
to  look  to  other  causes  for  the  source  of  light.  "  Luminescence  " 
does  not  require  a  high  temperature. 

604.  Distance  and  Distribution  of  Nebulae.  —  As  to  their  dis- 
tance, we  can  only  repeat  that  like  the  star-clusters  they  are 
within  the  star  universe  and  not  beyond  its  boundaries;  this 


STELLAR   SYSTEMS,    CLUSTERS,   AND   NEBULAE       559 

is  clearly  shown  by  the  "nebulous  stars,"  first  discussed  and 
pointed  out  by  the  older  Herschel,  and  by  such  peculiar  associ- 
ations of  stars  and  nebulae  as  we  find  in  the  Pleiades  (Fig.  196). 
Moreover,  in  certain  luminous  masses  known  as  the  "nubeculae" 
(near  the  south  pole  of  the  heavens),we  have  stars,  star-clusters, 
and  nebulae  promiscuously  intermingled.  In  the  sky  generally,  Their  distri- 
however,  the  distribution  of  the  nebulae  is  in  contrast  to  that  butlon  m 

the  heavens. 

of  the  stars.     The  stars  crowd  together  near  the  Milky  Way ;  They  mostly 
the  nebulae,  on  the  other  hand,  are  most  numerous  near  its  ayoidre- 
poles,  just  where  the  stars  are  fewest,  as  if  the  stars  had  some-  stars 
how  consumed  in  their  formation  the  substance  of  which  the  abound- 
nebulae   are  made,  or  as  if,  possibly,  on  the  other  hand,  the 
nebulae  had  been  formed  by  the  disintegration  of  stars,  —  as  a 
few  astronomers  have  maintained,  in  opposition  to  the  more 
common  view. 


THE   CONSTITUTION   OF   THE    SIDEEEAL   HEAVENS 

605.   The  Galaxy,  or  Milky  Way This  is  a  luminous  belt  The  Galaxy. 

of  irregular  width  and  outline  which  surrounds  the  heavens 
nearly  in  a  great  circle.  It  is  very  different  in  brightness  in 
its  different  parts,  and  in  several  constellations  is  marked  by 
dark  bars  and  patches  which  make  the  impression  of  overlying 
clouds;  the  most  notable  of  these  is  the  so-called  "coal-sack," 
near  the  southern  pole.  For  about  a  third  of  its  length  (from 
Cygnus  to  Scorpio)  the  Milky  Way  is  divided  into  two  nearly 
parallel  streams. 

The  telescope  shows  it  to  be  made  up  almost  wholly  of  small  A  belt  of 
stars  from  the  eighth  magnitude  down ;  it  contains  also  numer-  sma11  star& 
ous  star-clusters,  but  very  few  true  nebulae. 

Fig.  204  is  from  one  of  Barnard's  exquisite  small-scale  photo- 
graphs of  the  edge  of  the  Milky  Way  in  the  constellation  of 
Sagittarius.  With  a  powerful  telescope  the  star  clouds  would 
be  resolved  into  points  of  light. 


560 


MANUAL   OF   ASTRONOMY 


FIG.  204.  —  Star  Clouds  in  Edge  of  Milky  Way 

ecliptic  is  to  the  solar  system,  —  a  plane 
and  the  ground-plan  of  the  stellar  system, 

606,  Distribution  of  the 
Stars  in  the  Heavens.  —  It 
is  obvious  that  the  distribu- 
tion of  the  stars  is  not  even 
approximately  uniform; 
they  gather  everywhere  in 
groups  and  streams. 

Fig.  205  is  from  another  of 
Barnard's  photographs,  cover- 
ing parts  of  Scorpio  and  Ophiu- 
chus.  The  irregular  object  above 
and  a  little  to  the  right  of  the 
center  of  the  figure  is  the  faint 
star  p  Ophiuchi,  barely  visible 
to  the  naked  eye,  but  sur- 
rounded by  nebulosity  which, 
in  the  photograph,  makes  it  as 


The  Galaxy  inter- 
sects  the  ecliptic  at 
two  opposite  points 
not  far  from  the  sol- 
stices and  at  an  angle 
of  nearly  60°,  the 
northern  "  pole  of  the 
Galaxy "  being,  ac- 
cording to  Herschel, 
in  the  constellation  of 
Coma  Berenices. 

As  Herschel  re- 
marks, "  the  '  galactic 
plane'  is  to  the  side- 
real universe  much 
what  the  plane  of  the 
of  ultimate  reference, 


FIG.  205.  — Nebula  in  Ophiuchus 
Barnard 


STELLAR   SYSTEMS,    CLUSTERS,   AND   NEBULAE       561 

conspicuous  as  Antares  itself,  below  and  to  the  left,  — the  middle  one 
of  the  three.  The  dark  « lanes  "  and  other  starless  spaces  in  this  region 
are  very  remarkable. 

But  besides  this  the  examination  of  any  of  the  great  star- 
catalogues  shows  that  the  average  number  to  a  square  degree 
increases  rapidly  and  pretty  regularly  from  the  galactic  pole  to 
the  galactic  circle  itself,  where  they  are  most  thickly  packed. 
This  is  best  shown  by  the  "  star-gauges  "  of  the  elder  Herschel, 
each  of  which  consisted  merely  in  an  enumeration  of  the  stars 
visible  in  a  single  field  of  view  of  his  20-foot  reflector,  the  field 
being  15'  in  diameter. 

He  made  3400  of  these  "  gauges,"  and  his  son  Sir  John,  using  the  same  Most 

telescope,  followed  up  the  work  at  the  Cape  of  Good  Hope  with  2300  more  crowded 

in  the  south  circumpolar  regions.     From  the  data  of  these  star-gauges,  near 
Struve  has  deduced  the  following  figures  for  the  number  of  stars  visible  in       ,    ,. 

one  field  of  view :  .  circle. 


DISTANCE  FROM  GALACTIC  CIRCLE 

AVERAGE  NUMBER 
OF  STARS  IN  FIELD 

90°      

4  15 

60° 

6  52 

30°     

17  68 

0       

122  00 

607,   Structure  of  the  Stellar  Universe.  —  Herschel,  starting  structure  of 
from  the  unsound  assumption  that  the  stars  are  all  of  about  the  the  stellar 

,  ,  ,  universe. 

same  size  and  brightness  and  separated  by  approximately  equal 
distances,  drew  from  his  observations  certain  untenable  con- 
clusions as  to  the  form  and  structure  of  the  "  galactic  cluster," 
to  which  the  sun  was  supposed  to  belong,  —  theories  for  a  time 
widely  accepted  and  even  yet  more  or  less  current,  though  in 
many  points  certainly  incorrect. 

But  although  the  apparent  brightness  of  the  stars  does  not 
thus  depend  entirely  or  even  mainly  upon  their  distance,  it  is 
certain  that,  as  a  class,  the  faint  stars  are  smaller,  darker,  and 


562 


MANUAL   OF   ASTRONOMY 


more  remote  than  the  brighter  ones;  we  may,  therefore,  safely 
draw  a  few  conclusions,  which,  so  far  as  they  go,  in  the  main 
agree  with  those  of  Herschel  and  are  formulated  by  Newcomb, 
in  his  Popular  Astronomy,  substantially  as  follows : 

608,  (I)  The  great  majority  of  the  stars  we  see  are  contained 
within  a  space  having  roughly  the  form  of  a  rather  thin  flat 
disk,  like  a  thin  watch,  with  a  diameter  eight  or  ten  times  as 
great  as  its  thickness,  our  sun  being  not  far  from  the  center. 
In  other  words,  the  stars  which  compose  the  star  system  are 
spread  out  on  all  sides  in  or  near  a  widely  extended  plane,  pass- 
ing through  the  Milky  Way. 

(II)  Within   this   space   the  naked-eye   stars   are   distributed 
rather  uniformly,  but  with  some  tendency  to  cluster,  as  shown  in 
the  Pleiades.     The  smaller  stars,  on  the  other  hand,  are  strongly 
"  gregarious  "  and  are  largely  gathered  in  groups  and  streams, 
leaving  comparatively  vacant  spaces  between  them. 

(III)  At  right  angles  to  the  "  galactic  plane "  the  stars  are 
scattered  more  thinly  and  evenly  than  in  it,  and  we  find  here  on 
the  sides  of  the  disk  the  comparatively  starless  region  of  the 
nebulse. 

(IV)  As  to  the  Milky  Way  itself,  it  is  not  certain  whether 
the  stars  which  compose  it  form  a  sort  of  thin,  flat,  continuous 
sheet,  or  whether  they  are  ranged  in  a  kind  of  ring  or  in  spires, 
with  a  comparatively  empty  space  in  the  middle  where  the  sun 
is  placed. 

(V)  The  disk  described  above  does  not  represent  the  form  of 
the  stellar  system,  but  only  the  limits  within  which  it  is  mostly 
contained.    The  circumstances  are  such  as  to  prevent  our  assign- 
ing any  more  definite  form  to  the  system  itself  than  we  could 
assign  to  a  cloud  of  dust. 

As  to  the  size  of  the  disklike  space,  very  little  can  be  said 
positively,  but  it  seems  quite  certain  that  its  diameter  must  be 
at  least  as  great  as  from  ten  thousand  to  twenty  thousand  light- 
years,  —  how  much  greater  we  cannot  even  guess,  and  as  to 


STELLAR   SYSTEMS,   CLUSTERS,   AND   NEBULA       563 

what  is  beyond  we  are  still  more  ignorant.  If,  however,  there 
are  other  stellar  systems  of  the  same  order  as  our  own,  they  are 
neither  the  nebulae  nor  the  clusters  which  the  telescope  reveals, 
but  are  far  beyond  the  reach  of  any  instrument  at  present 
existing. 

609.  Do  the  Stars  form  a  System  ?  —  It  is  probable,  though  Question  as 
not  yet  absolutely  proved,  that  gravitation  operates  between  the  *°  wg^e^er 
stars  (as  indicated  by  the  motions  of  the  binaries),  and  they  are  form  a 
certainly  moving  very  swiftly  in  various  directions.     The  ques-  system- 
tion  is  whether  these  motions  are  governed  by  gravitation  and 

are  orbital  in  the  common  sense  of  the  word. 

There  has  been  a  very  persistent  belief  that  somewhere  there  Exploded 
is  "  a  great  central  sun,"  around  which  the  stars  are  all  circling.  ldea  of_ a 

central  sun. 

As  to  this,  there  is  no  longer  any  question ;  the  "  central  sun  " 
speculation  is  certainly  unfounded,  though  we  have  not  space 
here  for  the  demonstration  of  its  fallacy. 

Another  less  improbable  doctrine  is  that  there  is  a  general  revolution  of   Possible 
all  the  stars  around  the  center  of  gravity  of  the  whole,  —  a  revolution  nearly   revolution 
in  the  plane  of  the  Milky  Way.     Half  a  century  ago  Maedler,  in  his  specu-  ° 
lations  already  mentioned,  concluded  that  this  center  of  gravity  of  the   center  Of 
stellar  universe  was  near  Alcyone,  the  brightest  of  the  Pleiades,  and  that   gravity  of 
therefore  this  star  was  in  a  sense  the  "  central  sun."     Very  recently  (1900)   the  whole. 
Andre",  in  his  admirable  work  on  Stellar  Astronomy,  has  brought  this  theory 
again  into  favorable  notice,  showing  that  it  agrees  with  several  statistical 
facts  relating  to  the  proper  motions  of  the  stars.     He  even  goes  so  far  as 
to  deduce  from  the  data  (as  they  stand  at  present),  with  the  help  of  certain   Andrews  con- 
assumptions,  that  our  distance  from  the  "central  sun"  is  about  715  light-  elusion, 
years,  the  period  of  revolution  about  twenty-two  million  years,  and  the 
velocity  of  motion  about  36  miles  a  second.     But  the  evidence  of  any  such 
general  revolution  of  the  stars  is  very  far  from  conclusive,  and  the  data  are  so 
insufficient  that  the  numerical  results  are  not  entitled  to  much  confidence. 

610.  Indeed,  on  the  whole,  the  most  probable  view  still  seems  Probable 
to  be  that  the  stars  are  moving  much  as  bees  do  in  a  swarm,  ^^^ 
each  star  mainly  under  the  control  of  the  attraction  of  its  nearest  motions  are 
neighbors,  though  influenced  more  or  less,  of  course,  by  that  of  notorbltal- 


564 


MANUAL    OF    ASTRONOMY 


the  general  mass.  If  this  is  so,  the  paths  of  the  stars  are  not 
"  orbits  "  in  any  periodic  sense ;  i.e.,  they  are  not  paths  which 
return  into  themselves.  The  forces  which  at  any  moment  act 
upon  a  given  star  are  so  nearly  balanced  that  its  motion  must 
be  sensibly  in  a  straight  line  for  thousands  of  years  at  a  time, 
except  in  cases  where  two  stars  are  near  together. 

611,  Cosmogony.  —  One  of  the  most  interesting  and  one  of 
the  most  baffling  topics  of  speculation  relates  to  the  process  by 
which  the  present  state  of  things  has  come  about. 

In  a  forest,  to  use  an  old  comparison  of  Herschel's,  we  see 
around  us  trees  in  all  stages  of  their  life-history,  from  the  sprout- 
ing seedlings  to  the  prostrate  and  decaying  trunks  of  the  dead. 
Is  the  analogy  applicable  to  the  heavens,  and  if  so,  which  of  the 
heavenly  bodies  are  in  their  infancy  and  which  decrepit  with  age? 

At  present  many  of  these  questions  seem  to  be  absolutely 
beyond  the  reach  of  investigation.  Others,  though  at  present 
unsolved,  appear  approachable,  and  a  few  we  can  already 
answer.  In  a  general  way  we  may  say  that  the  condensation  of 
diffuse,  cloudlike  masses  of  matter  under  the  force  of  gravita- 
tion, the  conversion  into  heat  of  the  energy  of  motion  and  of 
position  (the  "kinetic"  and  "potential"  energy  —  Physics, 
p.  73)  of  the  particles  thus  concentrated,  the  effect  of  this  heat 
upon  the  mass  itself,  and  the  effect  of  its  radiation  upon  sur- 
rounding bodies,  —  these  principles  cover  nearly  all  the  explana- 
tions that  can  thus  far  be  given  of  the  present  condition  of  the 
heavenly  bodies. 

612.  Genesis  of  the  Planetary  System.  —  Our  planetary  sys- 
tem is  clearly  no  accidental  aggregation  of  bodies.     Masses  of 
matter  coming  haphazard  to  the  sun  would  move  (as  the  comets 
actually  do  move)  in  orbits  which,  though  always  conic  sections, 
would  have  every  degree  of  eccentricity  and  inclination.     In 
the  planetary  system  this  is  not  so.     Numerous  relations  exist 
for  which  the  mind  demands  an  explanation  and  for  which  gravi- 
tation does  not  account. 


STELLAR   SYSTEMS,    CLUSTERS,   AND   NEBULAE       565 

We  note  the  following  as  the  principal : 

(1)  The  orbits  of  the  planets  are  all  nearly  circular. 

(2)  They  are  all  nearly  in  one  plane  (excepting  those  of  some 
of  the  asteroids). 

(3)  The  revolution  of  all,  without  exception,  is  in  the  same  Facts  which 
direction.  indicate  » 

process  of 

(4)  There  is  a  curious  and  regular  progression  of  distances  evolution  IE 
(expressed  by  Bode's  Law,  which,  however,  breaks  down  with  the  solar 

^_  system. 

Neptune). 

As  regards  the  planets  themselves : 

(5)  The  plane  of  the  planet's  rotation  nearly  coincides  with 
that  of  the  orbit  (probably  excepting  Uranus). 

(6)  The  direction  of  rotation  is  the  same  as  that  of  the  orbital 
revolution  (excepting  probably  Uranus  and  Neptune). 

(7)  The  plane  of  the  orbital  revolution  of  the  planet's  sat- 
ellites coincides  nearly  with  that  of  the  planet's  rotation,  wher- 
ever this  can  be  ascertained. 

(8)  The  direction  of  the  satellites:  revolution  also  coincides 
with  that  of  the  planet's  rotation  (with  two  exceptions). 

(9)  The  largest  planets  rotate  most  swiftly. 

Now  this  arrangement  is  certainly  an  admirable  one  for 
a  planetary  system,  and  therefore  some  have  argued  that 
the  Deity  constructed  the  system  in  that  way,  perfect  from 
the  first.  But  to  one  who  considers  the  way  in  which  other  • 
perfect  works  of  nature  usually  attain  to  their  perfection  — 
their  processes  of  growth  and  development  —  this  explana- 
tion seems  improbable.  It  appears  far  more  likely  that  the 
planetary  system  was  formed  by  growth  than  that  it  was  built 
outright. 

613,   The  Nebular  Hypothesis.  —  The  theory  which  in  its  main  The  nebular 
features  has  been  very  generally  accepted,  as  supplying  an  intel-  hyp°the818- 
ligible  explanation  of  the  facts,  is  that  known  as  the  "  nebular 
hypothesis."     In  a  more  or  less  crude  and  unscientific  form  it 
was  first  suggested  by  Swedenborg  and  Kant,  and  afterwards, 


566 


MANUAL   OF   ASTRONOMY 


about  the  beginning  of  the  present  century,  was  worked  out  in 
mathematical  detail  by  Laplace.     He  maintained : 

(a)  That  at  some  time  in  the  past  the  matter  which  is  now 
gathered  into  the  sun  and  planets  was  in  the  form  of  a  nebula. 
But  there  was  no  assumption,  as  is  often  supposed,  that  matter 
was  first  created  in  the  nebulous  condition.     It  was  only  assumed 
that,  as  the  egg  may  be  taken  as  the  starting-point  for  the  life- 
history  of  an  animal,  so  the  nebula  is  to  be  regarded  as  the 
starting-point  of  the  life-history  of  the  planetary  system. 

(b)  This  nebula,  according  to  him,  was  a  cloud  of  intensely 
heated  gas.     (This  postulate  is  more  than  questionable.) 

(c)  Under   the    action    of   its    own   gravitation    the    nebula 
assumed  a  form  approximately  globular,  with  a  motion  of  rotation, 
the  rotational  motion  depending  upon  accidental  differences  in 
the  original  velocities  and  densities  of  different  parts    of  the 
nebula.     As   the   contraction    proceeded  the   swiftness  of  the 
rotation    would   necessarily   increase    for   mechanical    reasons, 
since  every  shrinkage  of  a  revolving  mass  implies  a  shortening 
of  its  rotation  period. 

(d)  In  consequence  of  the  rotation  the  globe  would  necessarily 
become  flattened  at  the  poles  and  ultimately,  as  the  contraction 
went  on,  the  centrifugal  force  at  the  equator  would  become  equal 
to  gravity  and  rings  of  nebulous  matter,  like  the  rings  of  Saturn, 

.  would  be  detached  (not  "  thrown  off")  from  the  central  mass.     In 
fact,  Saturn's  rings  suggested  this  feature  of  the  theory. 

(e)  The  ring  thus  formed  would   for  a  time   revolve   as    a 
whole,  but  would  ultimately  break,  and  the  material  would  col- 
lect into  a  globe  revolving  around  the  central  nebula  as  a  planet. 
Laplace  supposed  that  the  ring  would  revolve  as  if  solid,  the 
particles  at  the  outer  edge  moving  more  swiftly  than  those  at 
the  inner.     If  this  were  always  so,  the  planet  formed  would 
necessarily  rotate  in  the  same  direction  as  the  ring  had  revolved. 

(f)  The  planet  thus  formed  might  throw  off  rings  of  its  own 
and  so  form  for  itself  a  system  of  satellites. 


STELLAR   SYSTEMS,    CLUSTERS,    AND   NEBULA       507 

The  theory  obviously  explains  most  of  the  facts  of  the  solar  Explains  the 
system,  which  were  enumerated  in  the  preceding  article,  though  obvious 
some  of  the  exceptional  facts,  such  as  the  short  periods  of  the  not  centra- 
satellites  of  Mars  and  the  retrograde  motions  of  those  of  Uranus  dicted  b7 
and  Neptune,  cannot  be  explained  by  it  alone  in  its  original  seemun- 
form;   other  considerations   must  be  introduced.      Even   they,  favorable, 
however,  do  not  contradict  it,  as  is  sometimes  supposed. 

Many  things  also  make  it  questionable  whether  the  outer 
planets  are  so  much  older  than  the  inner  ones,  as  the  theory  would 
indicate.  It  is  not  impossible  that  they  may  even  be  younger. 

614.  On  the  whole,  we  may  say  that  while  in  its  main  out-  Probable 
lines  the  theory  probably  is  true,  it  also  probably  needs  serious  modlfica- 
modifications  in  details.     It  is  rather  more  likely,  for  instance,  needed, 
that  in  the  early  stages  the  nebula  was  a  cloud  of  ice-cold  mete- 
oric dust  than  an  incandescent  gas,  or  a  "  fire  mist,"  to  use  a  NO  original 
favorite  expression ;  and  it  is  likely  that  planets  and  satellites 

were  usually  separated  from  the  mother  orb  otherwise  than  in 

the  form  of   rings.     Nor  is   it  possible  that  a  thin  wide  ring  Rings  could 

could  revolve  in  the  same  wav  as  a  solid  coherent  mass :  the  uot  revolye 

m  manner 

particles  near  the  inner  edge  must  make  their  revolution  m  assumed  by 

periods  much  shorter  than  those  upon  the  circumference.  Laplace. 

A  most  serious    difficulty  arises    also  from   the    apparently 

irreconcilable  conflict  between  the  conclusions   as   to   the  age  Conflict  of 

and  duration  of  the  svstem,  which  are  based  on  the  theorv  of  conclusions 

J          as  to  age  of 

heat,  and  the  length  of  time  which  would  seem  to  be  required  system, 
by  the  nebular  hypothesis  for  the  evolution  of  our  system. 

Our  limits  do  not  permit  us  to  enter  into  a  discussion  of  Darwin's  "  tidal 
theory  "  of  satellite  formation,  which  may  be  regarded  as,  in  a  sense,  supple- 
mentary to  the  nebular  hypothesis ;  nor  can  we  more  than  mention  Faye's 
proposed  modification  of  it.  According  to  him,  the  inner  planets  are  the 
oldest. 

615.  The  Planetesimal,  or  Spiral  Nebula,  Hypothesis. — Accord-  Pianetesimai 
ing  to  a  theory  recently  proposed  and  developed  by  Chamberlin  hypot 
and  Moulton,  the  solar  system  was  at  one  time  in  ihc  form  of  a 


568  MANUAL  OF  ASTRONOMY 

spiral  nebula.  Such  a  nebula  is  supposed  to  have  been  made 
up  of  discrete  particles  ("planetesimals")  revolving  in  elliptical 
orbits  about  the  central  nucleus  and  across  the  arms  of  the  spiral 
rather  than  along  them.  The  arms  show  simply  the  distribution  of 
matter  at  a  given  time.  It  is  supposed  that  spiral  nebulse  may  be 
developed  by  tidal  disruption  when  two  suns  pass  near  each  other. 

According  to  this  hypothesis  the  sun  was  formed  from  the  cen- 
tral mass,  the  planets  from  the  local  condensations  or  nuclei  in 
the  coils  of  the  spiral,  their  masses  having  been  increased  by  the 
sweeping  up  of  the  scattered  particles  whose  orbits  they  crossed. 
In  a  similar  way  satellites  were  formed  from  smaller  nuclei. 

While  it  is  obviously  impossible  to  prove  absolutely  a  theory 
of  so  wide  application,  the  Planetesimal  Hypothesis  offers  some 
decided  advantages  over  the  Laplacian.  It  accounts  satisfactorily 
for  the  facts  in  harmony  with  the  older  theory  and  also  for  the 
direct  rotation  of  the  planets,  the  large  eccentricities  of  the 
orbits  of  Mercury,  Mars,  and  the  asteroids,  and  the  present  dis- 
tribution of  the  moment  of  momentum  of  the  solar  system. 
The  retrograde  motions  of  the  satellites  of  Uranus  and  Neptune 
offer  no  difficulty,  neither  do  the  rapid  revolutions  of  Phobos 
and  the  inner  portion  of  Saturn's  ring. 

The  fact  that  photography  has  shown  that  the  spiral  is  a 
common  form  of  nebula,  while  none  of  the  Laplacian  type  has 
been  found,  gives  added  weight  to  the  hypothesis.  We  must 
remember,  however,  that  the  solar  nebula  was  probably  much 
smaller  than  any  of  those  photographed. 

616.  Stars,  Star-Clusters,  and  Nebulae.  —  It  is  obvious  that 
the  nebular  hypothesis  in  all  of  its  forms  applies  to  the  explana- 
tion of  the  relations  of  these  different  classes  of  bodies  to  each 
star-clusters,  other.  In  fact,  Herschel,  appealing  only  to  the  "law  of  con- 
tinuity," had  concluded,  before  Laplace  formulated  his  theory, 
...,«;:  that  the  nebulae  develop  sometimes  into  clusters,  sometimes  into 

double  or  multiple  stars,  and  sometimes  into  single  stars.  He 
showed  the  existence  in  the  sky  of  all  the  intermediate  forms 


STELLAR   SYSTEMS,    CLUSTERS,    AND   NEBULA       569 

between  the  nebula  and  the  finished  star.  For  a  time,  about 
forty  years  ago,  while  it  was  generally  believed  that  all  the 
nebulae  were  nothing  but  star-clusters,  only  too  remote  to  be 
resolved  by  existing  telescopes,  his  views  fell  rather  into  abey- 
ance; but  they  regained  acceptance  in  their  essential  features 
when  the  spectroscope  demonstrated  the  substantial  difference 
between  gaseous  nebulae  and  the  star-clusters. 

£17.   Conclusions  from  the  Theory  of   Heat.  —  Kant  and  La-  Conclusions 
place,  .  as   Newcomb  says,  seem  to  have  reached  their  results  drawn  from 

TI.T  the  theory 

by  reasoning  forward.      Modern  science  comes  to  veiy  similar  Of  heat, 
conclusions  by  working  backward  from   the  present  state  of 
things. 

Many  circumstances  go  to  show  that  the  earth  was  once  much 
hotter  than  it  now  is.  As  we  penetrate  below  the  surface  the 
temperature  rises  nearly  a  degree  (Fahrenheit)  for  every  60  feet, 
indicating  a  white  heat  at  the  depth  of  a  few  miles  only;  the 
earth  at  present,  as  Sir  William  Thomson  says,  "  is  in  the  con-  The  earth 
dition  of  a  stone  that  has  been  in  the  fire  and  has  cooled  at  the  and  Planets 

.         ,,  once  hot. 

surface. 

The  moon  apparently  bears  on  its  surface  the  marks  of  the 
most  intense  igneous  action,  but  seems  now  to  be  entirely 
chilled. 

The  planets,  so  far  as  we  can  make  out  with  the  telescope, 
exhibit  nothing  at  variance  with  the  view  that  they  were  once 
intensely  heated,  while  many  things  go  to  establish  it.  Jupiter 
and  Saturn,  Uranus  and  Neptune,  do  not  seem  yet  to  have 
cooled  off  to  anything  like  the  earth's  condition. 

618,   Age  and  Duration  of  the  Solar  System.  —  In  the  sun  we  Age  and 
have  a  body  continuously  pouring  forth  an  absolutely  incon-  duratlonof 

J  J     L  J  the  solar 

ceivable  quantity  of  heat  without  any  visible  source  of  supply,  system, 
As  has  been  explained  already  (Sec.  275),  the  only  rational 
explanation  of  the  facts  thus  far  presented  is  that  which  makes 
it    a    huge    cloud-mantled    ball   of    elastic    substance    slowly 
shrinking  under  its  own  central  gravity,  and  thus  converting 


570  MANUAL   OF   ASTRONOMY 

into  the  kinetic  energy  of  heat l  the  potential  energy  of  its  par- 
ticles as  they  gradually  settle  towards  the  center.     A  shrinkage 
,     of  200  feet  a  year  in  the  sun's  diameter  (100  feet  in  its  radius) 
will  account  for  the  whole  annual  output  of  radiant  heat  and 
Assuming      light.      Looking  backward,   then,   and   trying  to   imagine  the 
the  suTand    course  °^  time  an(^  °f  events  reversed,  we  see  the  sun  growing 
planets  once  larger  and  larger,  until  at  last  it  has  expanded  to  a  huge  cloud 
cloud6 with     ^at  ^s  ^e  largest  orbit  of  our  system.     How  long  ago  this 
diameter        may  have  been  we  cannot  state  with  certainty.     If  we  could 
equal  to         assume  that  the  amount  of  heat  yearly  radiated  by  the  solar 

Neptune's 

orbit.  surface  had  remained  constantly  the  same  through  all  those  ages, 

and,  moreover,  that  all  the  radiated  heat  came  only  from  the 
slow  contraction  of  the  solar  mass,  apart  from  any  considerable 
original  capital  in  the  form  of  a  high  initial  temperature,  and 
without  any  reinforcement  of  energy  from  outside  sources,  — 

Assump-        IF  we  could  assume  these  premises,  it  is  easy  to  show  that  the 

doubtful  smi's  past  history  must  cover  about  fifteen  or  twenty  million 
years.  But  such  assumptions  are  at  least  doubtful;  radium 
and  its  congeners  may  have  played  an  important  part,  and  the 
sun's  age  may  be  many  times  greater  than  the  limit  we  have 
named. 

Prospect  for  Looking  forward,  on  the  other  hand,  from  the  present  towards 
ire<  the  future,  it  is  easy  to  conclude  with  certainty  that  if  the  sun 
continues  its  present  rate  of  radiation  and  contraction  and  receives 
no  subsidies  of  energy  from  without,  it  must  within  five  or  ten 
million  years  become  so  dense  that  its  constitution  will  be 
radically  changed.  Its  temperature  will  fall,  and  its  function 

1  So  far  we  have  no  decisive  evidence  whether  the  sun  has  passed  its  maxi- 
mum of  temperature  or  not.  Mr.  Lockyer  thinks  its  spectrum  (resembling  as 
it  does  that  of  Capella  and  the  stars  of  the  second  class)  proves  that  it  is  now  on 
the  downward  grade  and  growing  cooler,  and  the  fact  that  its  density  is  appar- 
ently much  higher  than  that  of  other  stars  —  at  least  than  that  of  the  variables 
of  the  Algol  type  (see  Sec.  582)  —  certainly  falls  in  well  with  the  idea  that  it  has 
reached  an  advanced  stage  of  development  and  perhaps  passed  its  culmination. 
But  the  evidence  can  hardly,  as  yet,  be  considered  conclusive. 


STELLAR    SYSTEMS,    CLUSTERS,    AND   NEBULA       571 

as  a  sun  will  end.  Life  on  the  earth,  as  we  know  life,  will 
be  no  longer  possible  when  the  sun  has  become  a  dark,  rigid, 
frozen  globe.  At  least  this  is  the  inevitable  consequence  of 
what  now  seems  to  be  the  true  account  of  the  sun's  present 
activity  and  the  story  of  its  life. 

At  the  same,  time  it  is  by  no  means  certain  that  the  processes  Possibility 
now  observed  have  been  going  on  steadily  through  all  the 
past,  or  will  continue  to  do  so  in  the  future,  without  break 
or  interruption.  Catastrophes  and  paroxysms,  sudden  changes 
and  reversals  of  the  course  of  events  at  critical  moments, 
are  certainly  possible  and  actually  occur,  as  the  phenomena 
of  the  solar  surface  and  temporary  stars  abundantly  make 
evident. 

619.   The  Present  System  not  Eternal. — One  lesson  seems  to 
to  be  clearly  taught :  that  the  present  system  of  stars  and  worlds 
is  not  an  eternal  one.     We  have  before  us  everywhere  evidence  The  system 
of  continuous,  irreversible  progress  from  a  definite  beginning  noteternal- 
towards   a  definite  end.      Scattered  particles  and  masses  are 
gathering  together  and  condensing,  so  that  the  great  grow  con- 
tinually larger  by  capturing  and  absorbing  the  smaller.     And  General 
yet,  on  the  other  hand,  the  phenomena  of  the  coronal  streamers,  aggregatlon 

J  .  .          of  scattered 

of  comets'  tails,  and  those  presented  by  the  swiftly  expanding  masses:but 
nebulosity  of  Nova  Persei,  seem  to  indicate  in  certain  cases  a  exceptions, 
process  exactly  the  reverse,  —  a  repulsion  and  dissipation  in 
space   of  finer  grained  materials,  possibly  the  "  ions "  of  the 
most  modern  physicists. 

At  the  same  time  the  hot  bodies  are  losing  their  heat  and 
distributing  it  to  the  colder  ones,  so  that  there  is  an  unremitting 
tendency  towards  a  uniform,  and  therefore  useless,  temperature  Dissipation 
throughout  our  whole  universe ;  for  heat  is  available  as  energy  of  ener^- 
(i.e.,  it  can  do  work)  only  when  it  can  pass  from  a  warmer  body 
to  a  colder  one.     The  continual  warming  up  of  cooler  bodies  at 
the  expense  of  hotter  ones  always  means  a  loss,  therefore,  not 
of  energy,  for  that  is  indestructible,  but  of  available  energy. 


572 


MANUAL   OF   ASTRONOMY 


'.  To  use  the  ordinary  technical  term,  energy  is  continually 
"dissipated"  by  the  processes  which  constitute  and  maintain 
life  on  the  universe.  This  "  dissipation  of  energy"  can  have 
but  one  ultimate  result,  that  of  absolute  stagnation  when  the 
temperature  has  become  everywhere  the  same. 

If  we  carry  our  imagination  backward,  we  reach  "  a  begin- 
nuig  of  things,"  which  has  no  intelligible  antecedent;  if  for- 
ward,  we  come  to  an  end  of  things  in  dead  stagnation.  That 
in  some  way  this  end  of  things  will  result  in  a  "new  heavens 
and  a  new  earth"  is,  of  course,  very  probable,  but  science  as  yet 
presents  no  explanation  of  the  method. 


EXERCISES 

1.  Find  the  mass  of  the  system  of  a  Centauri  from  the  data  given  in 
Tables  IV  and  VII;  namely,  parallax  (p)  =  0".75,  semi-major  axis  of 
orbit  (a"}  =  17".70,  and  period  (t)  =  81.1  years.     (See  Sees.  590  and  594.) 

Ans.    Mass  of  system  =  1.99  x  mass  of  the  sun. 

2.  Find  the  mass  of  the  system  of  Sirius  from  the  tabular  data. 

Ans.    3.01  x  mass  of  the  sun. 

3.  Find  the  mass  of  the  system  of  rj  Cassiopeiae  from  the  tabular  data. 

Ans.    2.10  x  mass  of  the  sun. 

4.  Find  the  mass  of  the  system  of  70  Ophiuchi  from  the  tabular  data. 

Ans.    2.92  x  mass  of  the  sun. 

NOTE.  —  The  results  obtained  by  the  solution  of  problems  1,  2,  3,  and  4  will  not 
agree  with  those  given  in  Sec.  590,  because  of  the  different  values  of  parallax 
employed.  The  discrepancies  fairly  illustrate  the  uncertainties  of  our  present 
knowledge. 

5.  Find  the  radius  of  the  apparent  orbit  of  the  spectroscopic  binary 
Lacaille  3105,  the  relative  velocity  of  the  components  being  385  miles  a 
second  and  the  period  3d2M6m,  as  indicated  by  the  doubling  of  the  lines 
in  the  spectrum.      Assume  that  the  orbit  is  circular,  that  its  plane  is 
directed  towards  the  sun,  and  that  the  two  components  are  equal. 

Ans.    Radius  of  orbit  =  16  493000  miles. 

6.  Compute  the  mass  of  the  system  on  the  same  assumptions  as  above, 
remembering  that  the  radius  of  this  apparent  orbit  is  also  the  radius  of  the 
relative  orbit  which  each  component  describes  around  the  other  regarded  as 
at  rest.  ^nSt   76.75  x  mass  of  the  sun. 


STELLAR  SYSTEMS,  CLUSTERS,  AND  NEBULAE   573 

7.  Carry  out  similar  computations  for  the  systems  of  £  Ursse  Majoris, 
/?  Aurigse,  and  p.  Scorpii,  using  the  data  of  Sec.  593. 

8.  Determine  the  radius  of  the  orbit  described  by  Spica  Virginis,  as 
shown  by  the  shift  of  the  lines  in  its  spectrum.     Velocity  =56.6  miles  a 
second;  period  =  4d19m.    Orbits  assumed  circular  and  in  plane  of  the  sun. 

Ans.    Radius  =  3  123500  miles. 

9.  From  this  determine  the  mass  of  the  system,  assuming  that  the  mass 
of  the  bright  star  is  infinitesimal  as  compared  with  that  of  the  dark  star, 
i.e.,  that  it  is  a  small  planet  revolving  around  a  dark  central  sun.     (A  very 
improbable  hypothesis,  of  course.)  AnSf    0.315  x  mass  of  the  sun. 

10.  What  is  the  mass  of  the  system  if  the  dark  star  is  equal  to  the 
bright  one?     (In  this  case  the  radius  of  the  relative  orbit  is  the  diameter 
of  the  apparent  orbit  of  Spica,  or  double  its  value  in  the  last  example.) 

Ans.    23  x  0.315,  or  2.520,  X  mass  of  the  sun. 

11.  What  is  the  mass  if  the  dark  star  has  a  mass  only  one  fourth  that 
of  the  bright  one?     (In  this  case  the  orbit  of  the  dark  star  has  a  radius 

4  times  as  great  as  that  of  Spica,  and  the  radius  of  the  relative  orbit  is 

5  times  as  great  as  that  of  the  apparent  orbit  of  Spica.) 

Ans.  53  x  0.315,  or  39.37,  x  mass  of  the  sun;  the  mass  of  the 
bright  star  being  31.50  and  that  of  the  dark  star  being  one  fourth  as 
great,  or  7.87. 

NOTE.  —  The  assumption  that  the  bright  star  is  a  small  planet,  revolving  around  a 
dark  central  body  vastly  more  massive  than  itself,  gives  us  a  minor  limit  to  the  pos- 
sible mass  of  the  system,  but  the  major  limit  cannot  be  fixed  without  knowledge  as 
to  the  relative  mass  of  the  dark  body. 

If  the  dark  body  is  larger  than  the  bright  one,  the  mass  of  the  system  cannot  exceed 
eight  times  that  minor  limit. 

The  general  formula  is  easily  obtained  :  let  n  be  the  ratio  between  the  masses  of 
the  bright  and  dark  stars,  so  that  if  r  is  the  radius  of  the  circle  described  by  the 
bright  star  around  the  common  center,  the  radius  of  the  circle  described  by  the  other 
will  be  nr,  and  the  radius  of  the  relative  orbit  will  be  (n  +  1)  r.  Also  let  M  be  the 
united  mass  of  the  two  stars.  Then,  expressing  the  period,  t,  in  years,  r  in  astronomi- 
cal units,  and  /*  ih  terms  of  the  sun's  mass,  we  have 


The  factor  (ra+1)3  becomes  unity  when  n=o,  —  i.e.,  when  the  bright  star  is  a 
particle  ;  and  infinity  when  n  becomes  infinite,  —  i.e.,  when  the  dark  star  is  a  particle 
revolving  at  the  infinite  distance,  r  (n  +  1).  It  becomes  8  when  n=  1,  the  two  stars 
being  equal. 

It  may  be  added  that  the  assumption  that  the  orbit  is  circular  and  that  its  plane 
passes  through  the  solar  system  is  entirely  gratuitous  and  not  likely  to  be  correct. 
But  the  general  character  of  the  results  would  not  be  seriously  changed  unless  the 
inclination  and  eccentricity  of  the  orbit  were  great,  as,  for  instance  (probably), 
in  the  case  of  Polaris. 


APPENDIX 

700.  Transformation  of  Astronomical  Coordinates.  —  It  is  often  neces- 
sary to  change  one  set  of  coordinates  into  another ;  to  convert,  for 
instance,  right  ascension  and  declination  into  altitude  and  azimuth 
or  into  latitude  and  longitude,  and  vice  versa.     The  process  is  a  sim- 
ple trigonometrical  calculation,  in  which  we  have  to  deal  with  spher- 
ical triangles  having  (usually)  given  two  sides  and  the  included  angle. 
There  are  various  methods  of  solution :  we  may  drop  a  perpendicu- 
lar from  one  of  the  unknown  angles  upon  the  opposite  side  and  carry 
out  the  solution  by  Napier's  rules  for  right-angled  triangles ;  or  we 
may  apply  Napier's  analogies  to  compute  the  two  unknown  angles  ; 
or,  finally,  we  may  use  an  auxiliary  angle,  as  indicated  in  Campbell's 
Practical  Astronomy. 

701.  To  convert  Right  Ascension  (a)  and  Declination  (8)  into  Alti- 
tude (h)  and  Azimuth  (A).  —  The  observer's  latitude,  <£,  must  also  be 
known  and  the  sidereal  time,  0.     Referring  to  Fig.  206,  we  see  that 
the  triangle  to  be  solved  is  OPZ,  in  which  we  have  PZ  =  90°  —  <£, 
PO  =  90°  —  8,  and  t,  the  hour  angle  ZPO,  =  (a  —  0).     Required  ZO 
or  s  (which  =  90°—  A),  and  the  angle  PZO  (which  is  the  supplement 
of  SZO,  the  azimuth  A). 

The  formulae  most  used  are  the  following  (Campbell's  Practical 
Astronomy,  Sec.  5): 

n  sin  N  =  sin  8  (a) 

n  cos  N  =  cos  8  cos  t        (b) 
whence,  tan  N  =  tan  8  sec  #. 

N  is  the  auxiliary  angle,  and  its  quadrant  is  determined  by  equa- 
tions (a)  and  (b),  which  give  the  signs  of  its  sine  and  cosine ;  n  is 
always  positive,  but  is  not  used. 

m,  tan  t  cos  N  tan  (d>  —  N) 

Then         tan  A  =  - — ; -,  and  tan  «  = *? L> 

sin  (<£  —  N)  cos  A 

Care  must  be  taken  to  observe  the  algebraic  signs  throughout. 

574 


APPENDIX 


575 


702.  To  convert  Right  Ascension  and  Declination  into  Latitude  and 
Longitude.  —  The  triangle  to  be  employed  is  OPP'  (Fig.  206),  in 
which  we  have  given  PP1  =  c,  the  obliquity  of  the  ecliptic  (23°  28'), 


PO  =  (90°  -  8),  and  P'PO  =  (90°  +  a).  P'PT  =  90°,  and  T  PM  = 
arc  T  M  =  right  ascension  of  0.  PP'O  =  (90°  -  X),  (X  =  angle  °K°  P'O), 
and  P'O  =  (90°  -  /3).  The  formulae  then  are: 

/  sin  F  =  sin  8  (c) 

f  cos  F  =  cos  8  sin  a     (d) 
tan  8 


whence 


sin  a 


Then     tan  X  =  -  — ^ — ->  and  tan  B  =  tan  (F  —  «)  sin  X. 

cos  F 

For  other  cases,  see  Campbell's  Practical  Astronomy  or  Went- 
worth's   Spherical  Trigonometry. 


576 


MANUAL   OF   ASTRONOMY 


703.  Projection  of  a  Lunar  Eclipse  (supplementary  to  Sec.  288).  — 
We  take  as  an  example  the  eclipse  of  Oct.  16,  1902,  which  will  be 
generally  visible  in  the  United  States. 

The  data,  as  given  in  the  American  Ephemeris,  are  : 


SUN 

MOON 

8°55'20".5   S. 
9".33 
V  55".  2   S. 
16'03".l 
8".  8 
right  ascension,  Oct 

9°  08'  52".  7   N. 
138«.31 
10'  06".  4  N. 
16'  08".  3 
69'  13".  2 
16,  18MOml2*.7. 

Hourly  motion  in  right  ascension 
Hourly  motion  in  declination  .     .     . 
Semidiameter    

Horizontal  parallax 

Greenwich  mean  time  of  opposition  in 

A  convenient  scale  is  1000"  to  the  inch;  this  will  bring  the 
figure  within  the  limits  of  an  8  x  10  sheet,  and  is  large  enough 
to  give  all  the  accuracy  required.  Fractions  of  a  second  of  arc 
are  neglected. 

The  work  is  made  easier  by  the  use  of  squared  paper,  but  the 
results  are  seldom  quite  as  precise,  because  of  the  inaccuracies  of 
the  ruling. 

704.  I.  The  first  step  is  to  lay  off  the  "  relative  orbit "  of  the  moon 
with  respect  to  the  shadow.  Draw  two  lines  accurately  perpendicu- 
lar to  each  other,  their  crossing  point  0  (Fig.  207)  being  the  place 
of  the  moon's  center  at  the  moment  of  opposition. 

(a)  On  the  horizontal  line  EW  lay  off  the  difference  of  the 
hourly  motions  of  the  sun  and  moon  in  right  ascension,  expressed 
in  seconds  of  arc  and  reduced  to  seconds  of  a  great  circle,  by  multiply- 
ing by  the  cosine  of  the  moon's  declination.     In  this  case  we  have 
(138.31  -  9.33)  x  15  x  cos  9°  08'  53",  which  equals  1910".     Ob  and 
Od  are  each  laid  off  with  this  value,  while  Oa  and  Oe  are  made  twice 
as  great. 

(b)  At  b  and  d  lay  off  perpendicular  to  the  line  EW  the  difference 
of  the  hourly  motions  in  declination  (the  shadow  moves  north  when 
the  sun  moves  south).     We  have  in  this  case  (10'  06".4  —  0'  55".2), 
which  equals  551".     We  lay  off,  therefore,  at  b  and  d  ordinates 
each  equal  to  551,  and  at  a  and  e  ordinates  twice  as  great. 


APPENDIX 


577 


Since  the  moon  is  moving  northwards,  the  ordinates  west  of  0 
must  be  laid  off  downwards,  and  east  of  0  upwards. 

If  the  work  has  been  carefully  done,  the  four  points  thus  plotted 
will  lie  accurately  on  a  straight  line  with  each  other  and  with  0,  and 
will  be.  the  points  occupied  by  the  moon's  center  one  and  two  hours 
before  and  after  opposition.  The  "hours"  on  this  line  are  to  be 
divided  into  halves  and  quarters,  and  wherever  necessary  the  fifteen- 
minute  spaces  can  be  divided  into  five-minute  portions. 

II.  Mark  the  center  of  the  shadow.  Lay  off  north  or  south  of  0  a 
distance  equal  to  the  difference  of  declination  of  the  moon  and  the 


FIG.  207.— Projection  of  a  Lunar  Eclipse 


shadow.  (The  declination  of  the  shadow  is  the  same  as  the  sun's 
with  its  sign  changed.)  In  this  case  we  have  OC  =  (9°  08'  52".7  — 
8°  55'  20". 5)  =  812",  —  to  be  laid  off  to  the  south  because  the  moon 
is  north  of  the  center  of  the  shadow. 

III.  Find  the  radius  of  the  shadow  and  draw  the  shadow. 
From  Fig.  208  we  see  that  MEN  (the  angular  semidiameter,  or 
"radius,"  of  the  shadow)  =  aNE  —  ACO  or  ECO.  But  ECO  = 
OEB  -  EBb,  so  that  MEN  =  aNE  +  EBb  —  OEB.  aNE  is  the 
horizontal  parallax,  P,  of  the  moon  ;  EBb  is  the  horizontal  parallax, 


578  MANUAL   OF   ASTRONOMY 

p,  of  the  sun ;  and  OEB  is  the  sun's  semidiameter,  S,  as  seen  from 
the  earth.  As  a  formula  this  is  written  p  =  f  £  (P  -\-p  —  S)  (the  f  ^ 
being  applied  to  take  account  of  the  slight  apparent  enlargement 
of  the  shadow  by  the  earth's  atmosphere).  In  this  case  we  have, 
therefore, 

p  =  «i  (59'  13".2  +  8".8  -  16'  03".  1)  =  2642". 

With  this  radius  and  C  as  a  center,  the  outline  of  the  shadow  may 
be  drawn,  but  it  is  not  necessary. 

IV.  Mark  the  points  on  the  relative  orbit  occupied  by  the  moon's 
center  at  the  moments  of  contact  with  the  shadow. 

(a)  To  the  radius  of  the  shadow  add  the  semidiameter  of  the 
moon  (in  this  case  2642"  +  968"  =  3610"),  and  with  this  distance 
as  a  radius,  from  C  as  a  center,  strike  two  arcs  cutting  the  relative 
orbit  at  I  and  II,  which  give  the  position  of  the  moon  at  the  two 
external  contacts. 

(b)  Subtract  the  moon's  semidiameter  from  the   radius  of   the 
shadow,  and  with   this  difference   (2642"  -  968"  =  1674")   as  a 


FIG.  208.  —  The  Earth's  Shadow 

radius,  from  C  as  a  center,  find  the  points  II  and  III  of  internal 
contact.  The  figure  may  be  completed  by  drawing  the  circles  to 
represent  the  moon,  using  I,  II,  M,  III,  and  IV  as  centers.  M,  the 
middle  of  the  eclipse,  is,  of  course,  half-way  between  II  and  III. 

V.  Finally,  read  off  the  times  of  contact  on  the  relative  orbit 
regarded  as  a  scale  of  time.  For  points  west  of  0  subtract  the 
time  readings  from  the  time  of  opposition  (18h10m.2  in  this  case), 
and  for  points  east  add  them. 


APPENDIX  579 

In  the  present  case  the  projection  as  figured  gives  the  following 
results  : 


I 

18  10  .2 

II 

18  10  .2 

M 

0h  6m.7 
18  10  .2 

III 

+  Oh38">.0 
18  10  .2 

IV 

18  10  .2 

16  17  .2 
(17.3) 

17  19  .2 
(19.0) 

18  03  .5 
.  (03.4) 

18  48  .2 
(47.9) 

19  49  .7 
(49.7) 

The  figures  in  parentheses  are  the  calculated  results  as  given  in  the  American 
Ephemeris. 

To  get  eastern  standard  time  subtract  5  hours ;  i.e.,  the  eclipse 
begins  at  Ilh17m.2,  E.S.T.,  its  middle  is  at  Ih03m.5  A.M.,  and  it  ends 
at  2h49m.7  A.M.,  being  total  from  12h19m.2  until  Ih48m.2  A.M. 

705.  Calculation  of  the  Eclipse.  —  This  is  very  simple,  the  triangles 
concerned  being  all  right-angled  plane  triangles.  Five-place  loga- 
rithms are  sufficient. 

I.  From  the  elements  given  in  the  Almanac,  form  the  following 
quantities : 

(a)  The  relative  hourly  motion  in  right  ascension  in  seconds  of  arc, 
reduced  to  arc  of  a  great  circle,  as  in  I  (a)  of  the  preceding  section  (Ob 
in  Fig.  207).     It  comes  out  1910".2  in  this  case.     (Beginners  are 
very  apt  to  forget  the  'multiplication  by  cosine  of  moon's  declination.) 

(b)  The  relative  motion  in  declination  (bt  in  the  figure),  551".2 
in  this  case. 

(c)  The  distance  of  the  center  of  the  shadow  from  the  point  of 
opposition  (the  line  OC  in  the  figure),  812".2  in  this  case. 

(d)  The  radius  of  the  shadow,  p  (the  line  CN  in  the  figure)  =  f  £ 
(P  +  p  -  SQ),  in  this  case  2642".2. 

(e)  The  distance  C,  I,  and  C,  IV  =  (p  +  S{)  =  3610".5  in  this 
case. 

(/)  The  distance  C,  II,  and  C,  III  =  (p  -  S£)  =  1673".9  in 
this  case. 

II.  In  triangle  Obt,  given  Ob  and  bt,  compute  the  angle  bOt  (=  i), 
and  the  hypotenuse  Ot,  the  orbital  relative  hourly  motion,     i  comes 
out  16°  5'.8  and  Ot,  1988 ".2  (but  only  its  logarithm  is  needed). 

III.  In    triangle    OCM,    given    OC    (812 ".2)    and    angle    OCM 
(i  =  16°  5'.8),  compute   CM   (780".4)  and   log   OM.      —  =  time 


580  MANUAL   OF   ASTRONOMY 

(in  hours)  by  which  the  middle  of  the  eclipse  differs  (earlier  in  this 

case)  from  the  time  of  opposition.     comes  out  6m.78,  giving 

(Jt 

18M)3m.4  for  the  middle  of  the  eclipse. 

IV.  In  the  triangle    CM,   I    (or   CM,   IV),   having   given   CM 
(780".4)  and  C,  I  (p  +  S<£,  i.e.,  2642".2  +  968".3  =  3610".5),  com- 
pute log  M,  I.     —~  is  the  time  (in  hours)  by  which  I  precedes  or 

\J~v 

IV  follows  the  middle  of  the  eclipse;  it  comes  out  1A773  or 
Ih468.4,  so  that  contact  I  occurs  at  16hl7™.0,  and  IV  at  19h49™.8. 

V.  In  the  triangle  CM,  II  (or  CM,  III),  having  given  CM  and 

C,  II  =  p  -  S{  (=  1673 ".9),  compute  log  M,  II.     ^7-^  =  time  by 

(Jt 

which  contacts  II  and  III  precede  and  follow  the  middle.  It 
comes  out  44m.70,  so  that  contact  II  occurs  at  17h18m.7,  and  III 
at  18*48«".l. 

The  slight  differences  between  these  results  and  those  given  in 
the  Ephemeris  are  probably  due  to  the  fact  that  the  latter  uses  for 
P)  T!  (P  +P  —  ^<L)>  instead  of  fj  of  the  same.  But  the  times 
cannot  be  observed  within  half  a  minute. 

It  should  be  noted  also  that  the  motion  of  the  moon  is  not  quite 
uniform,  either  in  right  ascension  or  declination  during  the  three 
and  a  half  hours  of  the  eclipse,  as  assumed  in  the  projection  and  cal- 
culation. It  would  greatly  complicate  the  matter  to  take  the  varia- 
tions into  account,  and  is  unnecessary,  considering  that  the  tenths 
of  a  minute  (which  alone  would  be  affected)  are  quite  below  the 
uncertainties  of  observation.  In  the  computation  of  a  solar  eclipse 
the  variations  would  have  to  be  included  j  but  that  subject  lies 
quite  beyond  our  scope. 


APPENDIX  581 


THE  GREEK  ALPHABET 


Letters 

Name 

Letters 

Name 

A,  a, 

Alpha. 

I,  i, 

Iota. 

B,  ft 

Beta. 

K,    K, 

Kappa. 

r>  7) 

Gamma. 

A,  A, 

Lambda. 

A,  8, 

Delta. 

M,  /x, 

Mu. 

E,  c, 

Epsilon. 

N,  v, 

Nu. 

Z,  £, 

Zeta. 

H,  £, 

Xi. 

HJ  17, 

Eta. 

0,  o, 

Omicron. 

®,*, 

Theta. 

H,    7T   0), 

Pi. 

Letters  Name 

P,  p  g,  Rho. 

2,  o-  s,  Sigma. 

T,  T,  Tau. 

Y,  v,  Upsilon. 

<£,  <£,  Phi. 

X,  x,  Chi. 

¥,  ^,  Psi. 

O,  w  Omega. 


MISCELLANEOUS   SYMBOLS 

cS  ,  Conjunction.  A.R.,  or  a,  Right  Ascension, 

a ,  Quadrature.  Decl.,  or  8,  Declination. 

<?  ,  Opposition.  X,  Longitude  (Celestial). 

& ,  Ascending  Node.  (3,  Latitude  (Celestial). 

£3 ,  Descending  Node.  <£,  (Terrestrial). 

°K° ,  Vernal  Equinox,  or  First  of  Aries. 
CD,  angle  between  line  of  nodes  and  line  of  apsides. 
e,  obliquity  of  ecliptic. 


DIMENSIONS    OF   THE   TERRESTRIAL   SPHEROID 

(According  to  Clarke's  Spheroid  of  1878.    For  the  spheroid  of  1866,  see  Sec.  134.) 

Equatorial  semidiameter,  — 

20  926202  feet  =  3963.296  miles  =  6  378190  meters. 
Polar  semidiameter,  — 

20  854895  feet  =  3949.790  miles  -  6  356456  meters. 
Mean  semidiameter,  i.e.,  J-  (2 a  -f-  #),  — 

20  902433  feet  =  3958.794  miles  =  6  370945  meters. 

Oblateness  (Clarke),  293.46  ;  (Harkness),  ^. 


Length  (in  meters)  of  1°  of  meridian  in  lat.  <j>  =  111132.09  -  556.05 
cos2</>  +  1.20  cos4<j!>. 


582  MANUAL   OP   ASTRONOMY 

Length  (in  meters)  of  1°  of  parallel  in  lat.  <£  =  111415.10  cos  <£ 

-  94.54  cos  3  <£. 

1°  of  lat.  at        pole  =  111699.3  meters  =  69.407  miles: 

1°  of  lat.  at  equator  ==  110567.2  meters  =  68.704  miles. 

These  formulae  correspond  to  the  Clarke  Spheroid  of  1866,  used 
by  the  United  States  Coast  and  Geodetic  Survey. 


TIME   CONSTANTS 

The  sidereal  day        =  23h  56m  48.090  of  mean  solar  time. 
The  mean  solar  day  =  24h  3m  568.556  of  sidereal  time. 

To  reduce  a  time-interval  expressed  in  units  of  mean  solar  time  to 
units  of  sidereal  time,  multiply  by  1.00273791 ;  log  of  0.00273791 
=  [7.4374191]. 

To  reduce  a  time-interval  expressed  in  units  of  sidereal  time  to 
units  of  mean  solar  time,  multiply  by  0.99726957  =  (1  —  0.00273043) ; 
log  0.00273043  =  [7.4362316]. 

Tropical  year  (Leverrier,  reduced  to  1900)     365d    5h  48m  458.51. 
Sidereal  year  «  «  «          365     6      9      8 .97. 

Anomalistic  year     "  «  «          365     6   13    48.09. 

Mean  synodical  month  (Neison)    ....  29d  12h  44m    28.864. 

Sidereal  month 27     7   43    11 .545. 

Tropical  month  (equinox  to  equinox)     .     .  27     7   43      4 .68, 

Anomalistic  month  (perigee  to  perigee)  .     .  27   13   18    37  .44. 

Nodical  or  draconitic  month  (node  to  node)  27     5     5    35  .81. 


Obliquity  of  the  ecliptic  (Newcomb), 

23°  27'  8".26  -  0".468  (t  -  1900). 

Constant  of  precession  (Newcomb),  50".248  +  0.000222  (t  -  1900). 
Constant  of  nutation  (Paris  Conference,  1896),  9".21. 
Constant  of  aberration  (Paris  Conference,  1896),  20".47. 
Solar  parallax  (Paris  Conference,  1896),  8 ".80. 
Velocity  of  light  (Michelson  and  Newcomb), 

186330  miles,  299860  km. 


APPENDIX 


583 


Major 
Planets 


ITer'striall 
Planets 


0 


•c-c^| 


'w  05 -a  < 

too  toi 


ss 

-1W 


•11 


mi 


3|« 

Bt« 


SYMBOL 


e 


pppp  I  p 

8< 
•o 


el 


»x 
1 


Oblate- 


Albedo 
(Mttller) 


Major 
Planets 


Ter'strial 
Planets 


m  i  en 

CO   '   R>  «O 


SFMBOL 


!§ 

' 


Is! 


584 


MANUAL  OF  ASTRONOMY 

TABLE  II.— THE   SATELLITES 


NAME. 

Discovery. 

Dist.  in  Equa- 
torial Radii 
of  Planet. 

Mean 
Distance  in 
Miles. 

Sidereal  Period. 

Moon 

60  27035 

238  840 

27<1      7h  43m  HB  5 

SATELLITES  OF 


1 

2 

Phobos    .... 
Deimos    .... 

Hall,                      1877 

2.771 
6.921 

5850 
14650 

7*  39"  15M 
1*     6   17    54.0 

SATELLITES  OF 


5 
1 

Nameless    .     .    . 
lo    .    .    . 

Barnard,               1892 
Galileo,                  1610 

2.551 
5.933 

112500 
261  000 

llh  57"  22».6 
lrt  18   27    33  5 

2 

Europa   .... 

9.439 

415000 

3    13   13    42.1 

3 

Ganymede  .     .    . 

«                                      u 

15.057 

664000 

7      3   42    33.4 

4 

Callisto  .... 

«                                  «( 

26.486 

1167000 

16    16  32    11.2 

6 

Nameless     .    .    . 

Perrine,                 1905 

162.92 

7185000 

253.4 

7 
8 

Nameless     .    .    . 
Nameless     .    .    . 

«                           « 
Melotte,                 1908 

167.86 

7403000 
16000000? 

260 

2.57 

SATELLITES  OF 


1 

Mimas     .... 

W.  Herschel,        1789 

3.11 

117000 

22b37">   5^.7 

2 

Enceladus   .    .    . 

" 

3.98 

157000 

Id     8   53      6.9 

3 

Tethys     .... 

J.D.  Cassini,        1684 

4.95 

186000 

1    21    18    25.6 

4 

Dione           .    .    . 

«            u                         u 

6.34 

238000 

2    17   41      9.3 

5 

Rhea  .             .    . 

"          "                 1672 

8.86 

332000 

4    12   25    11.6 

Titan 

Huyghens,             1655 

20.48 

771  000 

15    22   41    23.2 

7 

Hyperion    .    .    . 

G.  P.  Bond,            1848 

25.07 

934000 

21      G   39    27.0 

8 

lapetus  .... 

J.  D.  Cassini,        1671 

59.58 

2225000 

79      7   54    17.1 

9 

Phoebe    .... 

W.  Pickering,       1898 

213.5 

8000000 

546.5 

10 

Themis    .... 

1905 

24.3? 

906000? 

20    20? 

SATELLITES  OF 


1 

Ariel  

Lassell,                  1851 

7.52 

120000 

2d  12h  29">  2K1 

'2 

Umbriel  .... 

U 

10.46 

167  000 

4      3   27    37.2 

:; 

Titania    .... 

W.  Herschel,        1787 

17.12 

273000 

8    16  56    29.5 

4 

Oberon    .... 

»         *i                    « 

22.90 

365000 

13    11     7      6.4 

SATELLITE  OF 


1 

Nameless     .    .    . 

Lassell, 

1846 

12.93 

221500 

APPENDIX 


585 


OF  THE  SOLAR  SYSTEM. 


Synodic  Period. 

Inc.  of  Orbit 
to  Ecliptic 

Inc.  to  Plane  of 
Planet's  Orbit. 

Eccen- 
tricity. 

Diam'r 
in  Miles 

Mass  in 
Terms  of 
Primary. 

Remarks. 

29di2h44m    2».7 

5°    08'    40" 

- 

0.05491 

2162 

81.6 

Specific  gravity 

MAES. 


_                  _ 

26°    17'.2 

28°  * 

0 

35? 

? 

Orbits  sensibly 

coincident    with 

—                 — 

25     47.2 

28°  ± 

0 

10? 

9 

planet's  equator. 

JUPITER. 


2°    20'    23" 

_              _ 

? 

100? 

? 

* 

Id  igh  28">  35».9 

2     08       3 

- 

0 

2500 

.00001688 

3  13  17    53.7 
7     3   59    35.9 

1      38     57 
1     59     53 

- 

0 
.0013 

2100 
3550 

.00002323 

.00008844 

The  diameters 
are  Engelmann's. 
The  rest  of  the 

16  18     5      6.9 

1     57     00 

- 

.0072 

2960 

.00004248 

data  are  from 
Damoiseau. 

28°  4  (  to  plane  of 
planet's 

100? 

31  .4  (    equator 

40? 

SATURN. 


Long,  of  Ascend. 
Node  of  orbits 
on  ecliptic  for 
1900.  168°  10'  35". 

28°    10'    10" 

About  27°. 
Inclination  of  the 
5  inner  satellites 
to  plane  of  celes- 

0 
0 
0 
0 

600? 
800? 
1200? 
1100? 

The  planes  of 
the  5  inner  orbits 
sensibly  coincide 
with  the  plane  of 
the  ring. 

(5  inner  satellites 

" 

tial  equator 

0 

1500? 

? 

and  ring.) 

27     38     49 
27       4.8 
18     31.5 

=  6°  57'  43"  (1900) 

.0299 
.1189 
.0296 

3500? 
500? 
2000? 

*f 

(  Discovered  in- 
<  dependently  by 
(  Lassell. 

? 

5       6 

39     00? 

:    : 

.22 

50? 
30? 

? 

(On  photographs. 
(Retrograde. 
On  photographs. 

URANUS. 


Long,  of  Ascend. 

97°    61* 

0 

500? 

? 

Node  of  orbits  on 

«               u 

Inc.  to  celestial 

0 

400? 

? 

plane  of  ecliptic 

equator  75°  18' 

0 

1000? 

? 

All  Retrograde. 

=  165°  32'  (1900). 

«              « 

(1900). 

0 

800? 

? 

NEPTUNE. 


Long.  Asc.  Node, 

184°  25'  (1900). 

145°  12' 
=  -34°  48' 

120°  05'  (1900) 

0 

2000? 

9 

Retrograde. 

586 


MANUAL   OF   ASTRONOMY 


B  I 

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APPENDIX 


58T 


TABLE  IV  — STELLAR  PARALLAXES  AND  PROPER  MOTIONS 

(Kapteyn,  1901.) 


1 

NAME 

a  (1900) 

fi(1900) 

Mag. 

Paral- 
lax (p) 

I 

•s 

Dist. 

(light- 
years) 
<*) 

Proper 
Motion 
(fO 

Cross 
Motion 

i^xy 

(miles 
persec.) 

1 

') 

Groombridge  34  ... 
£  Tucanae  .  .  . 

Ohl2».7 
0  14  .9 

+  43e27' 
—  65  28 

7.9 
4.1 

0".30 
0  .15 

2 
2 

11.6 
21.7 

2".80 
2  .05 

29.4 
40.0 

3 

/3  Hydrse  

020  .5 

—  77  49 

2.7 

0  .14 

2 

23.3 

2  .28 

47.9 

4 

TJ  Cassiopeia^ 

043  .1 

+  57  17 

3.8 

0  .19 

2 

17.2 

1  .20 

18.5 

5 

G 

7 

iu.  Cassiopeia)  .... 
rCeti  
e  Eridani 

101   .6 
1  39  .4 
3  15    9 

+  54  26 
-16  28 
—  43  27 

5.4 
3.7 
4  4 

0  .11 
0  .32 
0    16 

2 
1 

o 

29.6 
10.2 
20  4 

3  .75 
1  .95 
3    03 

100.3 
17.9 

55.7 

'  R 

o2  Eridani 

4  10    7 

—  7  49 

4  7 

0    18 

o 

18  1 

4   05 

66.2 

9 
10 
11 

a  Tauri  (Aldebaran)  . 
Cordova  Z.  V.  243  .  . 
Sirius  

430  .2 

507  .7 
640  .8 

+  16  18 
-44  59 
—  16  35 

1.2 
8.5 
—  1.4 

0  .11? 
0  .32? 
0  .38 

1 

s 

29.6 
10.2 
8.6 

0  .19 
8.70 
1    31 

5.1 
80.0 
10.1 

12 

Procyon  

734  .1 

+  5  29 

0.7 

0    30 

o 

10.9 

1    25 

12.2 

13 
14 

10  Urste  Majoris  .  .  . 
LI  18115  ... 

854  .2 
9  07  .6 

+  42  11 
+  53  07 

4.2 
7.5 

0  .20 
0  .14 

2 

16.3 
23.3 

0  .50 
1  .69 

7.3 
35.6 

15 
16 
17 
18 

Arg.-Oeltzen  10603  .  . 
Groombridge  1646  .  . 
LI.  21185  
LI  21258 

1005  .3 
1021   .9 
1057  .9 
11  00    5 

+  49  58 
+  49  19 
+  36  38 
+  44  02 

7.0 
6.3 
7.5 
8  5 

0  .18 
0  .11 
0  .47 
0   24 

1 
1 

2 
3 

18.1 
29.6 
6.9 
13  6 

1  .43 
0  .89 
4  .75 
4    40 

23.4 
23.8 
29.7 
53  9 

19 
^0 

Groombridge  1830  .  . 
LI.  22954  . 

1147  .2 
12  10    0 

+  38  26 
—  9  44 

6.6 
60 

0  .15 
0    14 

1 
1 

21.7 
23.3 

7  .05 
1    02 

188.2 

21.5 

21 
22 

a  Centauri  
v'  Draconis  .... 

1432  .8 
1730  .2 

-60  25 

+  55  15 

0.9 

49 

0.76 

0    32 

4 
1 

4.3 

10.2 

3  .67 
0    16 

14.2 
1.5 

23 

24 
25 

°n 

Arg.-Oeltzen  17415  .  . 
70,  p,  Ophiuchi  .  .  . 
a  Lyrse  (Vega)  .... 

1737  .0 
1800  .4 
1833  .6 
19  45    9 

+  68  26 
+  2  31 
+  38  41 
+  8  36 

9.0 
4.2 
0.4 
1  i 

0  .25 
0  .16 
0  .15 
0   24 

2 
2 

2 

0 

13.1 
20.4 
21.7 
13  6 

1  .27 
1  .13 
0  .36 
0    65 

14.9 
20.8 
7.1 
80 

27 
2g 

61  Cygni  
e  Indi  .  . 

2102  .4 
21  55    7 

+  38  15 
—  57  12 

6.1 
4  8 

0  .41 

0   28 

4 
3 

8.0 
11  6 

5  .16 
4    68 

37.0 
49  1 

Of) 

Fomalhaut  . 

2252    1 

—  30  09 

1  4 

0    14 

1 

23  3 

0   35 

73 

30 

Lacaille9352  .... 
Polaris  

2259  .4 
1  18    5 

-36  26 

+  88  43 

7.1 
2  1 

0  .29 
0   074 

2 

3 

11.1 
44  0 

7  .00 
0   045 

71.0 
1.8 

Arcturus,  Canopus,  a  Orionis,  £  Orionis,  a  Cygni,  /3  Centauri,  and  y  Cassiopeiae,  all  of  them 
stars  of  the  first  or  second  magnitude,  have  also  been  carefully  observed  and  have  yielded 
no  parallax  exceeding  0".05. 

In  the  table  the  column  headed  "  weight "  indicates  roughly  the  probable  reliability  of 
the  parallax  given,  — the  estimate  depending  on  the  character,  number,  and  accordance  of 
the  different  determinations  for  the  star  in  question.  The  average  "  probable  error  "  for  the 
parallaxes  of  the  table  may  be  taken  as  about  0".04,  i.e.,  it  is  just  as  likely  as  not  that  an 
average  parallax,  weighted  2,  may  be  wrong  by  that  amount. 

With  several  of  the  stars  the  data  are  very  discordant  and  unsatisfactory,  so  that  it  is  to 
be  expected  that  ultimately  some  of  the  results  tabulated  above  will  prove  seriously  incor- 
rect ;  most  of  them  indeed  are  to  be  regarded  as  only  approximations  to  the  truth. 


588 


MANUAL   OF   ASTRONOMY 


APPENDIX 


589 


TABLE   VI  — VARIABLE    STARS 

(A  selection  from  Dr.  S.  C.  Chandler's  third  catalogue  (July,  1896)  containing 
such  as  are  visible  to  the  naked  eye,  have  a  range  of  variation  exceeding  half  a 
magnitude,  and  can  be  seen  in  the  United  States.) 


No. 

NAME 

Place,  1900 

Range  of 
Variation 
(mag.) 

Period 

(days) 

Remarks 

a 

S 

1 

TCeti      .... 

Ohl6°>.7 

-20°  37' 

5.1-  7.0 

65± 

Very  irreg. 

2 

R  Andromedse     . 

0   18  .8 

+  38     1 

5.6-12.8 

410.7 

3 

a  Cassiopeia?    .    . 

0   34  .5 

4-55  59 

2.2-  2.8 

Not  periodic 

4 

oCeti(Jfim)  .    . 

2    14  .3 

—  3  26 

1.7-  9.5 

331.6 

Large    irregu- 

larities in  date 

and  brightness 

5 

p  Persei  .... 

2   58  .8 

4-38  27 

3.4-  4.2 

33? 

Very  irreg. 

6 

/3  Persei  (Algol)  . 

3     1  .7 

+  40  34 

2.3-  3.5 

2d20h  48"  55".43 

Period  now 

shortening 

7 

\  Tauri    .... 

3   55  .1 

+  12   12 

3.4-  4.2 

3  22  52  12 

Algol  type 

irregular 

8 

e  Aurigse     .    .    . 

4   54  .8 

+  43  41 

3.0-  4.5 

Not  periodic 

9 

a  Orionis     .    .    . 

5   49  .7 

+    7  23 

0.7-  1.5 

Not  periodic 

10 

rj  Geminorum 

6     8  .8 

+  22  32 

3.2-  4.2 

231.4 

11 

£  Geminorum  .     . 

6   58  .2 

+  20  43 

3.7-  4.5 

10d3h4im30s.6 

12 

R  Canis  Majoris  . 

7    14  .9 

-16  12 

5.9-  6.7 

1  3  15    46 

Algol  type 

13 

R  Leonis  Minoris 

9    39  .6 

+  34  58 

6.0-13.0 

370.5 

14 

RLeonis     .    .     . 

9   42  .2 

+  11  54 

5.2-10.0 

312.8 

15 

UHydrae     .    .     . 

10    32  .6 

-12  52 

4.5-  6.3 

195  ±? 

Very  irreg. 

16 

R  Ursae  Majoris  . 

10   37  .6 

+  69   18 

6.0-13.2 

302.1 

17 

RHydrse     .    .    . 

13    24  .2 

-22  46 

3.5-  5.5 

425.15 

Period 

shortening 

18 

S  Virginia    .    .    . 

13    27  .8 

-   6  41 

5.7-12.5 

376.4 

19 

R  Bootis      .    .    . 

14    32  .8 

+  27   10 

5.9-12.2 

223.4 

20 

8  Librae   .... 

14    55  .6 

-   8     7 

5.0-  6.2 

2d  7h  5im  22».8 

Algol  type 

21 

R  Coronae    .    .    . 

15    44  .4 

+  28  28 

5.8-13.0 

Not  periodic 

22 

R  Serpentis     .    . 

15    46  .1 

+  15  26 

5.6-13.0 

357.0 

23 

a  Herculis   .    .    . 

17    10  .1 

+  14  30 

3.1-  3.9 

60*  to  90-1 

Not  periodic 

24 

U  Ophiuchi      .     . 

17    11  .5 

+    1   19 

6.0-  6.7 

2Qh  7m  423.56 

25 

u  Herculis  .     .     . 

17    13  .6 

+  33   12 

4.6-  5.4 

Irreg.  periodic 

26 

XSagittarii     .    . 

17    41  .3 

-27  48 

4.0-  6.0 

7d   oh  17m  57* 

27 

W  Sagittarii    .    . 

17    58  .6 

-29  35 

4.8-  5.8 

7   14  16   13 

28 

Y  Sagittarii     .    . 

18    15  .5 

-18  54 

5.8-  6.6 

5   18  33   24  .5 

29 

R  Scuti    .... 

18   42  .1 

-  5  49 

4.7-  9.0 

71.1 

Very  irreg. 

30 

ft  Lyraa    .... 

18   46  .4 

+  33   15 

3.4-  4.5 

12<*21h47m  23«.72 

31 

R  Lyras   .... 

18    52  .3 

+  43  49 

4.0-  4.7 

46.4 

32 

xCygni   .... 

19    46  .7 

+  32  40 

4.0-13.5 

406.02 

Period 

lengthening 

33 

TJ  Aquilse     .    .    . 

19    47  .4 

+   0  45 

3.5-  4.7 

7d   4hnm  593 

34 

S  Sagittae    .    .    . 

19    51  .4 

+  16  22 

5.6-  6.4 

8     9   11   48.5 

35 

X  Cygni  .... 

20    39  .5 

+  35   14 

6.4-  7.7 

16     9   15     7 

36 

TVulpeculse  .    . 

20   47  .2 

+  27  53 

5.5-  6.5 

4  10  27   50  .4 

37 

TCephei     .    .    . 

21      8  .2 

+  68     5 

5.2-10.7 

387 

38 

,xCephei      .    .    . 

21    40  .4 

+  58   19 

4.0-  5.5 

430  ± 

Irreg.  periodic 

39 

SCephei       .    .     . 

22    25  .4 

+  57  54 

3.7-  4.9 

5d  gh  47m  39».3 

40 

ft  Pegasi  .... 

22    58  .9 

+  27  32 

2.2-  2.7 

Not  periodic 

41 

R  Aquarii    .     .    . 

23    38  .6 

-15  50 

5.8-11? 

387.16 

42 

R  Cassiopeise  .    . 

23   53  .3 

+  50  50 

4.8-12 

429.5 

590 


MANUAL   OF   ASTRONOMY 


CO       XI 


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APPENDIX 


591 


TABLE   VIII —  MEAN   REFRACTION 

(Corresponding  to  temperature  of  50°  F.,  and  to  a  barometric  pressure  of  29.6  inches.) 


Altitude 

Refraction 

Altitude 

Refraction 

Altitude 

Refraction 

0° 

34'  50" 

11° 

4'  47".  7 

30° 

1'  39".  5 

1 

24  22 

12 

4  24  .5 

35 

1   22  .1 

2 

18  06 

13 

4  04  .4 

40 

1   08  .6 

3 

14  13 

14 

3  47  .0 

45 

57  .6 

4 

11  37 

16 

3  18  .2 

50 

48  .3 

5 

9  45 

18 

2  55  .5 

55 

40  .3 

6 

8  23 

20 

2  37  .0 

60 

33  .2 

7 

7  19 

22 

2  21  .6 

65 

26  .8 

8 

6  29 

24 

2  08  .6 

70 

20  .9 

9 

5  49 

26 

1  57  .6 

80 

10  .2 

10 

5  16 

28 

1  48  .0 

90 

0  .0 

For  every  5°  F.  by  which  the  temperature  is  less  than  50°  F. ,  add  one  per 
cent  to  the  tabular  refraction,  and  decrease  it  in  the  same  ratio  for  temperatures 
above  50°  F. 

Increase  the  tabular  refraction  by  three  and  a  half  per  cent  for  every  inch  of 
barometric  pressure  above  29.6  inches,  and  decrease  it  in  the  same  ratio  below 
that  point.  These  corrections  for  temperature  and  pressure,  though  only 
approximate,  will  give  a  result  correct  within  2",  except  in  extreme  cases. 


COMSTOCK'S  FORMULA  FOR  REFRACTION 

9836    ^ 

r"  — tan  f. 

460  +  t 

6  is  the  barometer  reading  in  inches ;  t,  the  temperature  in  degrees  Fahren- 
heit ;  f,  the  apparent  zenith-distance.  The  error  of  the  formula  is  less  than  1" 
for  zenith-distances  under  75°,  except  in  extreme  conditions  of  temperature  and 
pressure. 


INDEX 


All  references  are  to  Sections,  not  to  Pages,  unless  expressly  so  stated. 


In  the  personal  statistics  the  years  of  birth  and  death  are  both  given  when  known 
to  the  writer.    A  single  date  followed  by  a  dash  indicates  that  the  person  was  born 

in  that  year,  but  is  known  or  believed  to  be  living ;  ( ? )  indicates  that  he  is 

still  living,  but  that  the  year  of  birth  has  not  been  ascertained.  A  single  date  not 
followed  by  a  dash  indicates  that  the  person  was  living  and  active  at  that  time,  but 
is  no  longer  living,  though  dates  of  birth  and  death  have  not  been  ascertained. 


Aberration,  constant  of,  172;  Paris  con- 
ference, value,  page  582. 

Aberration  of  light,  defined  and  illus- 
trated, 171;  determination  of  the 
velocity  of  the  earth  and  its  distance 
from  the  sun,  173. 

Absolute  temperature  and  zero,  272,  note ; 
method  of  determining  stellar  paral- 
lax, 549;  scale  of  star  magnitudes, 
557. 

Absorption,  of  light  and  heat  by  solar  at- 
mosphere, 266;  atmospheric,  of  solar 
heat,  268. 

Acceleration,  by  gravitation,  146;  equa- 
torial of  the  sun's  surface,  230 ;  secu- 
lar, of  the  moon, 329 ;  of  Encke's  comet, 
490. 

Acetylene,  perhaps  present  in  comets,  498. 

Achromatic  telescope,  44. 

Adalberta,  an  asteroid,  420. 

ADAMS,  J.  C.  (1819-92),  English  mathe- 
matical astr.,  457,  525. 

Adjustments  of  the  transit  instrument,  63. 

Aerolite,  see  Meteorite. 

JEthra,  an  asteroid,  421. 

Age  and  duration  of  solar  system,  618. 

Albedo,  defined,  210,  384;  of  Moon,  210; 
Mercury,  395 ;  Venus,  400 ;  Mars,  411 ; 
Ceres  and  Vesta,  422;  Jupiter,  432; 
Saturn,  446;  Uranus,  455;  Neptune, 
459. 

ALBRECHT,  T.  (? ),  German  geod- 

esist,  94. 

Alcyone  (i)  Tauri),  Maedler's  central  sun, 
544. 

Aldebaran  (a  Tauri),  a  typical  first-mag- 
nitude star,  557. 


Algol  (|8  Persei),  its  variability,  etc.,  580, 
582. 

Algol  stars,  limiting  density  of,  594. 

ALLEN,  R.  H.  (1838-1906),  532. 

Almucantars,  defined,  14;  the  instru- 
ment, 67,  92. 

Alpha  Centauri,  parallax  of,  545,  548; 
light  compared  with  the  sun's,  564; 
double-star  orbit  of,  590;  Table  VII, 
page  590. 

Alpha  Orionis,  or  Betelgeuze,  its  irregu- 
lar variability,  574. 

Alphabet,  Greek, ,page  581. 

ALPHONSO  X,  King  of  Leon  and  Castile 
(1221-84),  359. 

Altair  (a  Aquilse),  a  typical  first-magni- 
tude star,  557;  its  light  compared 
with  that  of  the  sun,  562. 

Altazimuth  instrument,  70. 

Altitude,  defined,  15,  29;  of  sun,  lati- 
tude by,  90,  112;  time  by,  103. 

Altitudes,  of  circumpolar  stars,  latitude 
by,  88;  meridian,  of  stars,  for  lati- 
tude, 89;  circummeridian,  latitude 
by,  91 ;  equal,  method  of,  for  time, 
102. 

ANDRE,  C.  (? — — -),  French  astr.,  428, 
609. 

Andromache,  an  asteroid,  421. 

Andromeda,  Nova  in,  575;  nebula  of, 
599,  600,  602. 

Andromedes,  see  Bielids. 

Angle,  position,  585. 

Annual  equation  of  the  moon,  the,  328  (6). 

Annual  motion  of  sun,  the  apparent, 
155. 

Annular  eclipses,  290;  nebulae,  599, 
600. 

Anomalistic  year,  the,  182. 


594 


MANUAL    OF   ASTRONOMY 


Anomalous  refraction,  shift  of  spectrum 
lines  by,  256. 

Anomaly,  orbital,  denned,  160,  163. 

Apex  of  the  sun's  way,  543. 

Aphelion  denned,  160. 

Aplanatic  object-glass,  45. 

Apogee  defined,  195. 

Apsides,  line  of,  defined,  160 ;  revolution 
of  earth's,  164 ;  of  moon's,  195,  327  (2). 

ARCHIMEDES  (287  B.C.),  Greek  philoso- 
pher; lunar  crater,  219. 

Arcturus  (a  Bootis) ,  discovery  of  its  prop- 
er motion,  537 ;  its  magnitude,  558 ; 
heat  from,  563. 

Areas,  equal,  law  of,  in  earth's  orbital 
motion,  162 ;  in  moon's,  195 ;  demon- 
strated, 303,  304;  in  planetary  orbits, 
307. 

Arequipa  Observatory,  its  Bruce  tele- 
scope, 536;  discovery,  on  its  photo- 
graphs, of  variable  stars,  583;  of 
variable-star  clusters,  584;  of  spec- 
troscopic  binaries,  593. 

ARGELANDER,  F.  (1799-1875),  German 
astr.,531,532,  note,  533,  536,  555,  557. 

Ariel,  innermost  satellite  of  Uranus, 
456. 

Aries,  first  of,  22,  23,  167. 

ARISTARCHUS  (270  B.C.),  Greek  astr., 
464;  lunar  crater,  221. 

ARISTOTLE  (384  B.C.),  Greek  philosopher, 
481 ;  lunar  crater,  221. 

Artificial  horizon,  74. 

\scension  Island,  467. 

Ascension,  right,  defined,  24,  26,  29. 

Asteroids,  the,  348,  418-428 ;  designation, 
418 ;  discovery  of  first  five,  418 ;  meth- 
ods of  search,  419;  orbits,  420,  421; 
dimensions,  422 ;  mass  and  density, 
423;  number,  424;  origin,  425. 

Astraea,  discovery  of,  418. 

Astrology,  a  pseudo-science,  5. 

Astronomical  latitude  defined,  32,  87, 
138  (1). 

Astronomische  Gesellschaft,  the,  its  star- 
catalogues,  533. 

Astronomy,  branches  of,  3 ;  rank  among 
sciences,  4;  utility,  5;  place  in  edu- 
cation, 6. 

Atlases,  star,  Argelander's,  Heis', 
Klein's,  Upton's,  532,  note. 

Attraction,  of  gravitation,  its  law,  143; 
of  spheres,  144 ;  acceleration  by,  146 ; 
total  between  sun  and  earth,  226. 

Augmentation  of  moon's  semidiameter, 
81. 

Aurora  borealis,  periodicity  following 
that  of  the  sun-spots,  243. 

Axes,  semi-major,  of  planetary  orbits 
unchangeable  by  secular  perturba- 
tions, 376. 

Azimuth,  defined,  16,  29;  determination 
of,  115. 


B 


BABINET,  J.  (1794-1872),   French  astr., 

505. 
BAILEY,  S.  I.  (1854 ),  American  astr. 

at  Arequipa,  584,  593. 
BALL,  SIR  ROBERT  (1840 ),  English 

astr.,  346. 
BARNARD,  E.   E.  (1857 ),  American 

astr.,  422,  449,  459,  504,  605. 
Barometer,  effect  of  its  rise  or  fall  upon 

the  rate  of    a  clock,  55;    upon  the 

tides,  343. 
BAYER,  J.    (1572-1625),    German    astr., 

532,  574  (1). 

BELOPOLSKY,  A.  ( ? ),  Russian  astro- 
physicist, 403,  450,  542,  592. 

Belts,  of  Jupiter,  433;  of  Saturn,  446; 
of  Uranus,  455. 

BIELA,  W.  (1782-1856),  Austrian  officer ; 
his  comet,  484,  494,  502,  524,  526. 

Bielid  meteors,  the,  521,  522,  524,  526,  527. 

Binaries,  spectroscopic,  591-593. 

Binary  stars,  586-595;  number  of,  586; 
discovery  of ,  586 ;  orbits  of ,  586-590; 
mass  of,  594;  also  note  to  Exercises, 
page  573. 

BESSEL,  F.  W.  (1784-1846),  German  astr., 

533,  548,  551,  589. 

Beta  Aurigae,  spectroscopic  binary,  593. 
Beta  Librae,  its  probable  diminution  of 

brightness,  574  (1). 
Beta  Lyrae,  its  spectroscopic  behavior, 

581,  592;  variables  of  this  type,  581. 
Bethlehem,  Star  of,  575. 
BODE,  J.  E.  (1747-1826),  German  astr., 

349,  418. 
BOND,  G.  P.   (1826-65),  second  director 

of  Harvard  Observatory,  449. 
BOND,  W.  C.  (1789-1859),  first  director 

of  Harvard  Observatory,  222,  447, 452, 

504. 
BORRELLY,  A.  (? ),  French  astr., 

498. 
BOUGUER,  P.    (1698-1758),  French  astr., 

210. 
BOYLE,  R.  (1627-91),  English  physicist, 

277. 
BOYS,  C.  V.  (? ),  English  physicist, 

145,  153,  563. 
BRADLEY,  J.  (1692-1742),  English,  third 

Astronomer  Royal,  171,  440. 
BRAKE,  see  Tycho. 
BREDICHIN,    TH.    (1831-1904),    Russian 

astr.,  501. 

Bright-line  spectra,  their  origin,  247. 
Brightness,  relative,  of  stars  of  different 

magnitude,  558 ;  stellar,  causes  of  dif- 
ference in,  565. 
BROOKS,  W.  (1844 ),  American  astr., 

479,  502. 
BRUCE,  Miss  C.  (died  1900),  American 

patron  of  science,  419,  536, 


INDEX 


595 


Bruce  photographic  telescope,  of  Heidel- 
berg, 419,  600 ;  of  Arequipa,  536,  571 ; 
spectrograph  of  Yerkes  Observatory, 
page  505. 

BRUNNOW,  F.  (1821-91),  American  and 
German  astr.,  540. 

BUNSEN,  R.  (1811-99),  German  chemist, 
245,  246,  248,  498. 

Burning  lens,  the,  273. 


C-ESAR,  AUGUSTUS  (63  B.C.-A.D.  14),  184. 

C^ESAR,  JULIUS  (100  B.C.-44  B.C.),  184. 

Calcium,  present  in  sun-spots  and  f  aculae, 
253;  in  chromosphere  and  promi- 
nences, 257 ;  its  H  and  K  lines  in  spec- 
trum of  temporary  stars,  576. 

Calculation,  of  a  lunar  eclipse,  288,  704 ; 
of  a  solar,  296. 

Calendar,  the,  183-186. 

Calorette,  the,  or  small  calory,  267. 

Calory,  the,  denned,  267. 

CALLANDREAU,  O.  (1852-1904),  French 
astr.,  486,  487. 

Camera,  prismatic,  252,  263. 

CAMPBELL,  W.  W.  (1862 ),  third 

director  of  Lick  Observatory,  80,  82, 
409,  450,  542,  576,  592,  700,  702. 

"  Canals  "  of  Mars,  412,  413. 

Canon  of  Eclipses,  The,  Oppolzer's,  296. 

Capella  (a  Aurigse),  its  magnitude,  558; 
a  spectroscopic  binary,  592. 

Capture  of  Leonids  by  Uranus,  527. 

"Capture  theory"  of  periodic  comets, 
486. 

Carbon  and  diamonds  in  meteorites, 
509. 

CARRINGTON,  R.  (1826-75),  English 
amateur,  229,  230. 

CASSEGRAIN  (1670),  French  optician,  49. 

CASSINI,  G.  DOMINIC  (1625-1712),  first 
director  of  Paris  Observatory,  403, 
447,  452,  464. 

CASSINI,  JACQUES  (1677-1756),  son  of 
G.  D.,  second  director  of  Paris  Observ- 
atory, 449. 

Cassiopeiae,  Nova,  575. 

Castor,  probable  decrease  of  brightness, 
574  (1) ;  a  spectroscopic  binary,  592. 

Catalogues,  of  stars,  533,  534;  of  star- 
spectra,  572;  of  variable  stars,  583; 
Table  VI,  page  589. 

CAVENDISH,  H.,  Lord  (1731-1810),  Eng- 
lish physicist,  148. 

Celestial  sphere,  infinite,  7. 

Centauri,  «,  cluster  of,  584,  598. 

Central  motion,  laws  of,  303-306. 

Central  sun,  the,  544,  609. 

Centrifugal  force  due  to  earth's  rotation, 
129,  130. 

Ceres,  discovery  of,  418 ;  diameter,  mass, 
etc.,  422,  423. 


CHANDLER,  S.  C.  (1846 ),  American 

astr.,  92,  94,  583. 
CHARLES  (about  1810),  French  physicist, 

277. 

CHARLOIS,M. (1864-1910), French  astr.419. 
Charts,  star,  536. 
CHAUVENET,    W.    (1819-70),    American 

mathematician,  82,  92. 
Chicago,  tide  at,  344. 
Chromosphere,  the,   257-259,   279;    and 

prominences,   how  observed    at   any 

time  by  spectroscope,  258,  259. 
Chronograph,  the,  59 ;  Hough's  printing, 

Chronometer,  the,  57 ;  longitude  by,  107, 

112,  114. 
Circle  of  position    (Sumner's   method), 

113. 
CLAIRAUT,  A.  C.  (1713-65),  French  astr., 

136. 

CLARK,  ALVAN  (1808-87),  American  opti- 
cian, 51. 
CLARK,  A.  G.  (1832-96),  son  of  A  Ivan, 

51,  589. 

CLARK,  G.  B.  (1827-91),  son  of  Alvan,  51. 
CLARKE,  COL.  A.  R.  (1828 ),  English 

geodesist,  134;  Appendix,  page  581. 
Classification  of  variable  stars,  573. 
CLAVIUS,   C.    (1537-1612),   Italian   astr., 

185 ;  lunar  crater,  221. 
CLERKE,   Miss   A.   M.   (1842-1907),  253, 

423,  540,  581. 
CLERK-MAXWELL,  J.  (1831-79),  English 

physicist,  449,  502. 
Clock,  astronomical,  55 ;  error  and  rate 

defined,  56. 

Clock,  driving,  for  telescope,  53. 
Clusters,  variables  in,  584;  of  stars,  598. 
Coelostat,  the,  54. 
Collimating  eyepiece,  69. 
Collimation,  line  of,  and  its  adjustment, 

63. 

Collimator  of  spectroscope,  244. 
Collision  of  comet,  with  earth,  the  proba- 
ble effect,  505 ;  with  sun,  506. 
Collisions,   astronomical,   causing    light 

and  heat,  576,  577,  581,  603,  615. 
Color  of  sunlight  modified  by  absorption 

in  solar  atmosphere,  266. 
Colors  of  stars,  560 ;  of  double  stars,  585. 
Colures  defined,  23. 
Coma  Berenices,  the  pole  of  the  Galaxy. 

605. 
Comet,  great,  of  1882  (Donati's),  476, 478, 

480,  487,  493,  499,  501,  504. 
Cometary  and  meteoric  orbits,  relation 

between  them,  526. 
Comet-families,  485,  486. 
Comet-groups,  487. 
Comets,    476-506;    their    number,    477; 

designations,    478;    discovery,    479; 

duration  and  brightness,  480 ;  orbits, 

481,  482;     elements    of    orbit,    483; 


596 


MANUAL   OF   ASTRONOMY 


elliptic  comets,  484;  short-period 
comets  and  comet-families,  485;  cap- 
ture of  comets,  486;  disintegration 
of,  486,  502,  524 ;  comet-groups,  487 ; 
orbital  statistics,  488 ;  origin  of  com- 
ets, 489;  acceleration  of  Encke's, 
490 ;  physical  character,  491 ;  constit- 
uent parts,  492;  dimensions,  493; 
mass,  494;  density,  495;  probable 
nature,  496 ;  light  and  spectrum,  497, 
498 ;  phenomena  exhibited  when  near 
the  sun,  499:  formation  of  tail,  500, 
501 ;  repulsive  force  of  sun,  502 ;  anom- 
alous phenomena,  503 ;  photography 
of  comets,  504;  danger  from,  505, 
506. 

COMMON,  A.  A.  (1841-1903),  English  engi- 
neer, 51. 

Common  motions  of  stars,  538. 

Companion,  dark,  of  Algol,  582;  faint,  of 
Sirius  and  of  Procyon,  589. 

Comparison  of  spectra,  method  of,  249. 

Compensation  pendulums,  55. 

COMSTOCK,  G.  C.  (1855 ),  American 

astr.,  82,  487,  page  591. 

Conies,  the,  314,  315. 

Conjunction,  denned,  190,  352. 

Constancy,  of  solar  heat,  274 ;  secular,  of 
the  major  axes  and  periods  of  planet- 
ary orbits,  164,  376. 

Constant,  of  aberration,  172,  page  582; 
of  gravitation,  145;  of  precession, 
165,  page  582;  solar,  267;  of  light- 
equation,  441 ;  of  nutation,  page 
582. 

Constellations,  the,  531 ;  distortion  of,  by 
proper  motion,  540. 

Constitution,  of  the  earth's  interior,  154 ; 
of  the  sun,  277-280;  of  comets,  496, 
498. 

Contacts  of  transit  of  Venus  observed 
for  solar  parallax,  469-471. 

Continuous  spectrum,  given  under  what 
conditions,  247;  of  Holmes'  comet, 
498 ;  of  Nova  Aurigae,  576 ;  of  certain 
nebulae,  602. 

Contraction  of  sun,  explaining  mainte- 
nance of  its  radiation,  275. 

Coordinates,  celestial,  tabular  exhibit  of 
the  different  systems  in  use,  29 ;  trans- 
formation of,  701,  702. 

COPERNICUS,  N.  (1473-1543),  Polish  astr., 
124,  360 ;  lunar  crater,  215,  219. 

Cordova  star-catalogue  and  zones,  533. 

Corona,  solar,  the,  262-264,  280. 

Coronae  Borealis,  Nova,  575. 

CORTIE,    A.    (? ),    English    astr., 

Cosmogony,  611. 
Cotidal  lines,  339,  340. 
Counter  glow,  or  Gegenschein,  the,  430. 
Criterion  for  distinguishing  stars  opti- 
cally double,  586. 


Cross  or  "  thwartwise  "  motion  of  a  star, 

540. 
Curvature,  of  earth's  surface,  measured, 

123 ;  of  earth's  orbit,  226. 
Cygni,  Nova,  575. 


DALTON,  J.  (1766-1844),  English  physi- 
cist, 277. 

Danger  from  comets,  505-506. 

Dark  lines  in  spectra,  due  to  absorption, 
247. 

Dark  stars,  582,  589,  597. 

DARWIN,  G.  H.  (1845 ),  English 

mathematician,  346,  614. 

Date-line,  the,  111. 

DAWES,  W.  R.  (1799-1868),  English  ama- 
teur, 46,  234,  447. 

Day,  sidereal  and  solar,  25,  96,  97 ;  civil 
and  astronomical,  100 ;  the  beginning 
of,  111 ;  invariability  of,  128. 

Declination,  parallels  of,  20;  denned,  21, 
29. 

Degrees,  of  astronomical  latitude,  their 
varying  length,  133;  of  latitude  and 
longitude,  formulae  for  their  length, 
pages  581,  582. 

Deimos,  a  satellite  of  Mars,  416. 

DE  LA  RUE,  W.  (1815-89),  English  ama- 
teur, 222,  233. 

DELISLE,  J.  (1688-1768),  French  astr., 
471. 

DENNING,  W.  F.  (? ),  English  ama- 
teur, 523. 

Density,  of  earth,  151-153 ;  of  moon,  201 ; 
of  sun,  228;  of  planets,  how  deter- 
mined, 382;  Mercury,  392;  Venus, 
398;  Mars,  408;  Jupiter,  432;  Saturn, 
445;  of  Uranus,  455;  Neptune,  459; 
of  Algol  system,  582;  limiting,  of 
Algol-type  variables,  594. 

Designation,  of  asteroids,  418 ;  of  comets, 
478;  of  stars,  532;  of  variable  stars, 
583. 

DESLANDRES,  H.  (? ),  French  spec- 

troscopist,  261,  450. 

DE  Vico,  F.  (1805-48),  Italian  astr.,  403, 
page  586. 

Dhurmsala,  meteorite  of,  extremely  cold, 
512. 

Diameter,  angular  and  real,  relation 
between,  10;  of  moon,  199;  of  sun; 
224 ;  of  planets,— Mercury,  392 ;  Venus, 
398 ;  Mars,  408 ;  asteroids,  422 ;  Jupi- 
ter, 432;  Saturn,  445;  Uranus,  455; 
Neptune,  459,  also  Table  I,  Appendix, 
page  583;  of  comets,  493;  diameters 
of  stars,  566 ;  of  Algol,  582. 

Diameter  of  a  planet,  how  determined, 
379 

Differences  of  stellar  brightness,  causes 
for,  565. 


INDEX 


597 


Differential  method  for  determining 
place  of  a  celestial  object,  116,  117; 
for  stellar  parallax,  550,  551. 

Diffraction,  its  effect  upon  telescopic 
definition,  46. 

Diffraction  grating,  the,  244. 

Dimensions,  of  the  earth,  133,  134, 
581;  of  comets,  493;  of  stars, 
582 ;  of  binary  star  orbits,  590. 

Dione,  fourth  satellite  of  Saturn,  452. 

Dip  of  the  horizon,  13,  77. 

Direction,  of  earth's  orbital  motion  at  any 
moment,  516 ;  of  sun's  motion  in  space, 
543. 

Disappearance,  periodical,  of  Saturn's 
ring,  448. 

Disintegration  of  comets,  502 ;  of  meteoric 
swarms,  528. 

Disk,  spurious,  of  stars  in  telescope,  46 ; 
sun's  relative  brightness  of  different 
parts,  233,  266. 

Displacement  of  lines  in  spectrum,  of 
sun,  254-256;  of  stars,  541,  542;  in 
spectrum  of  temporary  star,  576,  577 ; 
of  spectroscopic  binaries,  592. 

Dissipation  of  energy,  618,  619. 

Distance,  apparent  and  real  diameters  of 
an  object,  relation  between  them,  10 ; 
distance  and  parallax,  their  relation, 
78 ;  equation  for,  545. 

Distance  of  a  planet  from  sun,  geometri- 
cal method  of  determination,  371. 

Distance  of  sun  from  earth,  determined 
by  velocity  of  light  combined  with 
constant  of  aberration,  173;  by  con- 
stant of  light-equation,  442;  other 
methods,  Chapter  XV,  463-475. 

Distortion  of  disks  of  sun  and  moon  near 
horizon,  83. 

Distribution,  of  sun-spots  on  solar  disk, 
239;  of  nebula?  in  heavens,  604;  of 
stars,  606-608. 

Disturbing  force,  the,  323. 

Diurnal  circles,  or  parallels  of  declina- 
tion, 18,  20. 

Diurnal  rotation  of  the  heavens,  18. 

DOERFEL,  G.  S.  (1643-88),  German  astr., 
481 ;  a  lunar  crater,  219. 

DONATI,  G.  B.  (1827-73),  Italian  astr.; 
his  comet  of  1858,  476,  478,  480,  493, 
499,  501,  504. 

DOPPLER.  C.  (1803-53),  German  physicist, 
254. 

Doppler-Fizeau  principle,  shift  of  spec- 
trum lines  by  radial  motion,  254,  255 ; 
applied  to  rotation  of  Venus,  403 ;  to 
Saturn's  rings,  450;  to  star  motions, 
541,  542,  543,  576,  582,  588,  note,  591, 
592,  593. 

Double  stars,  585,  595 ;  colors  of,  585 ;  dis- 
tance and  position  angle,  585 ;  optical 
and  physical,  586.  See  also  Stars, 
Binary. 


Doubling  of  lines,  in  spectrum  of  tempo- 
rary stars,  576,  577 ;  in  spectroscopic 
binaries,  593. 

DOWNING,  A.  M.  (1850 ),  English 

astr.,  525. 

Draconitic  or  nodical  month,  192,  paqe 
582. 

DRAPER,  H.  (1837-82),  American  astro- 
physicist, 504,  570,  572,  600. 

DRAPER,  MRS.  H.  (? ),  572. 

Draper  Catalogue  of  spectra,  572. 

Drawings,  of  the  corona  unsatisfactory, 
262 ;  of  nebula?,  600. 

DUNER,  N.  C.  ( ? ),  Swedish  spectro- 

scopist,  230,  581,  592. 

Duration,  of  a  lunar  eclipse,  285 ;  of  solar 
eclipses,  292 ;  of  transit  of  Venus,  405 ; 
future  of  the  sun,  618. 

Durchmusterung ,  Argelander's  northern, 
530,  533,  536 ;  Schoenfeld's  southern, 
533 ;  Cape  of  Good  Hope  photographic, 
533. 

Dyne  and  megadyne,  scientific  units  of 
force  (stress),  142. 


Earth,  the,  —  leading  astronomical  facts, 
119;  globularity  of,  120;  its  approxi- 
mate diameter,  121-123;  its  rotation 
demonstrated,  124-127 ;  invariability 
of  rotation,  128,  345,  396;  centrifugal 
force  due  to  rotation,  129-131 ;  effect 
on  form  of  earth,  130,  134;  form  of, 
132 ;  geodetic  method  of  determining 
its  dimensions,  133-135;  form  alone 
by  pendulum  observations  and  purely 
astronomical  methods,  136;  station 
errors,  137;  latitudes,  astronomical, 
geographical  and  geocentric,  138 ;  sur- 
face and  volume,  139;  mass  and  den- 
sity, determination  of,  140-152 ;  mass 
and  force,  140-142;  gravitation,  143, 
144,  145,  146;  mass  and  force  distin- 
guished, 141 ;  scientific  units  of  force, 
142;  the  Cavendish  experiment,  148- 
153;  constitution  of  interior,  154; 
accepted  dimensions,  Appendix,  page 
581. 

Earth's  orbital  motion  and  consequences, 
the,  —  apparent  annual  motion  of  sun, 
155;  the  ecliptic,  etc.,  156;  the  zodiac, 
157;  form  of  orbit,  158,  159;  the  el- 
lipse, 160 ;  eccentricity  of  orbit  discov- 
ered, 161 ;  law  of  orbital  motion,  162, 
163 ;  changes  in  orbit,  164 ;  precession, 
165-169;  nutation,  170;  aberration, 
171-173 ;  orbital  velocity  determined, 
173 ;  the  equation  of  time,  174-177 ;  the 
seasons,  178-181 ;  the  three  kinds  of 
year,  182 ;  the  Calendar,  183-186 ;  the 
Metonic  cycle  and  golden  number, 
187 ;  the  Julian  period  and  epoch,  188. 


598 


MANUAL   OF   ASTRONOMY 


Earth's  shadow,  dimensions  of,  282,  283, 
285,  703,  704. 

Earth's  surface,  area  of,  139;  parabolic 
velocity  at,  319. 

Earth-shine  on  the  moon,  206. 

Eccentricity,  of  an  orbit,  defined,  160, 
315,  363;  expression  for,  in  terms  of 
body's  actual  velocity  and  the  para- 
bolic velocity,  320,  note. 

Eccentricity  and  inclinations  of  orbits 
oscillate  under  perturbation,  164,  376. 

Eclipse  variables  of  Agol  type,  580. 

Eclipse  year,  the,  297. 

Eclipses,  lunar,  282-288,  703-704;  solar, 
289-296;  Oppolzer's  canon  of,  296; 
yearly  number  of,  297 ;  relative  num- 
ber of  lunar  and  solar,  298 ;  recurrence 
of,  the  Saros,  299 ;  of  Jupiter's  satel- 
lites, 439-441;  of  lapetus,  Saturn's 
satellite,  449. 

Ecliptic,  the,  defined,  23,  156;  poles  of 
ecliptic,  27,  156;  obliquity  of,  156; 
change  of  obliquity,  164,  Appendix, 
page  582;  effect  of  obliquity  in  pro- 
ducing equation  of  time,  176. 

Ecliptic  limits,  lunar,  286 ;  solar,  293. 

Educational  value  of  astronomy,  6. 

Effects  of  meteors  upon  terrestrial  con- 
ditions, 520. 

Electric  lamp,  energy  per  candle-power, 
519. 

Elements,  chemical,  detected  in  sun,  250 ; 
in  comets,  498 ;  in  meteorites,  509 ;  in 
shooting-stars,  518 ;  in  stars,  567 ;  in 
nebulae,  602. 

Elements  of  an  orbit,  of  a  planet,  362 ;  of 
a  comet,  483 ;  of  the  planets,  Table  I, 
Appendix,  page  583;  of  comets  of 
short  period,  Table  III,  Appendix, 


Ellipse,  definitions  relating  to  the,  160, 
314,  315 ;  the  instantaneous,  324. 

Elliptic  comets,  482^86. 

Ellipticity,  see  Oblateness. 

ELLIS,  W.  (? ),  English  astr.,  243. 

Elongation,  defined,  190,  352. 

ENCKE,  J.  F.  (1791-1865),  German  astr., 
464 ;  his  comet,  484,  490,  493. 

End  of  the  present  system,  618, 619. 

Energy  of  solar  radiation,  270,  271 ;  con- 
sumed by  electric  lamp,  519. 

Engine,  Ericsson's  solar,  270. 

Enlargement,  apparent,  of  sun  and  moon 
near  horizon,  9. 

Envelopes  in  head  of  comets,  492,  499. 

Epicycloidal  motion  of  planets  relative 
to  earth,  354. 

Epsilon  Lyrse,  quadruple  star,  457,  585, 
597. 

Equal  altitudes,  determination  of  time, 
102. 

Equalization,  method  of,  in  photometry, 
560  (2). 


Equation,  personal,  64 ;  of  time,  99,  174- 
177 ;  Clairaut's,  136 ;  of  the  equinox, 
169;  showing  the  relation  between 
the  species  of  an  orbit,  and  the  actual 
and  parabolic  velocities,  320;  annual, 
of  the  moon,  328  (6) ;  for  determining 
the  mass  of  a  planet  by  means  of  its 
satellite,  380;  of  light,  440;  for  the 
mass  of  a  binary  system,  594. 

Equations  connecting  difference  of  stellar 
magnitude  with  ratios  of  brightness, 
558. 

Equator,  celestial,  or  equinoctial,  defined, 
20. 

Equatorial  parallax,  80;  acceleration  of 
solar  surface,  230. 

Equatorial  telescope,  mounting  of,  52 ; 
coude  (elbowed),  54;  use  in  deter- 
mining place  of  celestial  object,  117. 

Equinoctial  circle,  the,  or  celestial  equa- 
tor, 20. 

Equinoxes,  defined,  23;  precession  of, 
165-168 ;  equation  of,  169. 

ERATOSTHENES  (276-196  B.C.),  Alexan- 
drian astr.,  122 ;  lunar  crater,  221. 

ERICSSON,  J.  (1803-89),  Swedish- Amer- 
ican inventor,  270,  272. 

ERMAN,  P.  (1764-51),  German  physicist, 
525. 

Eros  (asteroid),  periodic  changes  of 
brightness,  383,  428 ;  rotation  period, 
383,  428;  discovery,  426;  orbit,  427; 
observed  for  solar  parallax,  427,  468 ; 
diameter  and  rotation,  428 ;  possible 
duplicity,  428. 

Error,  or  correction,  of  clock  defined,  56 ; 
of  computed  orbit  of  Neptune,  458. 

Eruption  theory  of  temporary  stars,  581. 

Eruptions,  solar,  260. 

Eruptive  or  metallic  prominences,  260. 

Establishment,  the,  of  a  port,  331. 

Eta  Argus  (or  Carinae),  its  irregular  vari- 
ability, 574  (2). 

Evection,  lunar,  the,  328  (4). 

Evolution,  tidal,  346,  614;  of  binary  star 
systems,  595. 

Exercises,  Chapter  I,  pages  30-31 ;  Chap- 
ter II,  page  65 ;  Chapter  III,  page  75 ; 
Chapter  IV,  pages  103,  104 ;  Chapter 
V,  pages  134,  135 ;  Chapter  VI,  pages 
164,  165 ;  Chapter  IX,  pages  259,  260 ; 
Chapter  XI,  pages  293,  294 ;  Chapter 
XII,  pages  344,  345 ;  Chapter  XV,  page 
408;  Chapter  XVI,  pages  453,  454; 
Chapter  XVIII,  pages  504,  505 ;  Chap- 
ter XIX,  pages  535,  536 ;  Chapter  XX, 
pages  572,  573. 

Extinction,  method  of,  in  photometry, 
560  (1). 

Eye  and  ear,  method  of  observation, 
58. 

Eyepiece,  collimating,  69;  or  ocular, 
various  forms,  47. 


INDEX 


599 


F 


FABRICIUS,  D.  (1564-1617) ,  German  astr., 
578. 

Faculae,  solar,  233,  237,  253. 

Fall  of  meteors,  507,  510,  517,  521. 

Families,  comet,  485,  486. 

FAYE,  H.  (1814-1902),  French  astr.,  230, 
242,  614. 

FIZEAU,  H.  L.  (1819-96),  French  physi- 
cist ;  the  Doppler-Fizeau  principle,  254, 
255,  256,  403,  450,  541-544,  591-593. 

FLAMMARION,  C.(1842 ),  French  astr., 

413,  417,  540. 

FLAMSTEED,  J.  (1646-1719),  first  Astron- 
omer Royal,  532 ;  lunar  crater,  221. 

Flash  spectrum,  the,  at  eclipse,  252. 

FLEMING,  MRS.  (1857-1911),  Harvard 
Observatory,  576,  583. 

Force,  scientific  units  of,  142 ;  disturbing, 
the,  323 ;  tide-raising,  the,  332-335. 

Form,  spheroidal,  of  earth,  its  determina- 
tion, 132-136. 

Formula,  for  dip  of  the  horizon,  77;  for 
geocentric  parallax,  79;  for  refrac- 
tion, 82,  page  591;  for  latitude  by 
zenith  telescope,  92;  for  time  from 
single  altitude  of  sun,  103;  for  eccen- 
tricity of  an  orbit,  in  terms  of  the 
actual  and  parabolic  velocities,  320, 
note ;  for  semi-major  axis  of  orbit,  in 
terms  of  U  and  V,  320 ;  for  velocity  at 
any  point  in  its  orbit,  Ex.  12,  page  294 ; 
for  cross  or  "  thwartwise  "  motion  of 
star,  540 ;  for  distance  of  a  star  in 
terms  of  its  parallax,  545;  in  light- 
years,  547 ;  for  mass  of  a  binary  sys- 
tem, 594. 

Formulae  for  areal,  linear,  and  angular 
velocities  in  central  motion,  305. 

FOUCAULT,  L.  (1819-68),  French  physi- 
cist, 125-127. 

Fractional  and  negative  star  magni- 
tudes, 558. 

FRAUNHOFER,  J.  (1787-1826),  German 
optician,  246,  247,  567. 

FROST,  E.  B.  (1866 ),  director  of  Yer- 

kes  Observatory,  255,  542. 

Fundamental  star-catalogues,  533. 


Galaxy,  the,  605. 

Gale's  comet  of  1894,  504. 

GALILEO,  G.  (1564-1642),  Italian  astr., 
55,  219,  399,  438,  447. 

GALLE,  J.  G.  (1812-1910),  German  astr., 
457. 

Gaseous  nebulae,  their  spectrum,  602; 
their  greenish  hue,  602. 

GASSENDI,  P.  (1592-1655),  French  astr. ; 
lunar  crater,  215,  219. 

GAUSS,  C.  F.  (1777-1855),  German  mathe- 
matician, 365,  418. 


Gegenschein,  or  "counter"  glow,  the, 
430. 

Geissler  tube,  245,  248. 

Geocentric,  parallax,  78-80;  latitude, 
138  (3) ;  place  of  a  planet,  368. 

Geodetic  method  of  determining  earth's 
dimensions  and  form,  133-135. 

Geographical  latitude,  138  (2). 

Geometrical  method  for  determining  a 
planet's  distance  from  earth  and  sun, 
371 ;  for  the  solar  parallax,  465-472. 

Georgium  Sidus,  Herschel's  name  for 
Uranus,  453. 

GILL,  SIR  DAVID  (1843 ),  director  of 

Cape  of  Good  Hope  Observatory  (now 
retired),  467,  468,  504. 

Globe,  celestial,  description  and  rectifi- 
cation, 37,  38. 

Gnomon,  the,  93,  165  (3),  note. 

GODFREY,  T.  ( ? 1749),  American  opti- 
cian, 75. 

Golden  number,  the,  187. 

GOTHARD,  E.  (1857-1909),  Hungarian 
astr.,  602. 

GOULD,  B.  A.  (1824-96),  American  astr., 
531,  533. 

GRAHAM,  G.  (1665-1751),  English  mech- 
anician, 54,  55. 

Grating,  diffraction,  the,  244. 

Gravitation,  law  of,  143;  formulae  for, 
144,  146 ;  constant  of,  145 ;  theory  of, 
Newton's  preliminary  verification  by 
means  of  moon's  motion,  312. 

Gravitational  methods  of  determining 
the  solar  parallax,  473,  474. 

Gravity,  affected  by  centrifugal  force 
due  to  earth's  rotation,  130;  distin- 
guished from  earth's  attraction,  131 ; 
on  surface  of  moon,  201 ;  on  sun,  227 ; 
on  Mercury,  392;  on  Venus,  398;  on 
Mars,  408 ;  on  asteroids,  423 ;  on  Jupi- 
ter, 432;  on  Saturn,  445;  on  Uranus, 
455;  on  Neptune,  459.  See  also  Table 
I,  page  583. 

Greek  alphabet,  page  581. 

GREEN,  N.  E.  (1823-99),  English  artist 
and  amateur,  411. 

Gregarious  tendency  of  stars,  540. 

Gregorian  Calendar,  the,  185,  186. 

Gregorian  telescope,  the,  49. 

GREGORY  XIII,  Pope  (1502-85),  Italian, 
185. 

GREGORY,  J.  (1638-75),  Scotch  astr.,  49. 

GRIMALDI,  F.  M.  (1618-63),  Italian  astr.  ; 
lunar  crater,  221. 

GROOMBRIDGE,  S.  (1755-1832),  English 
astr.,  539. 

Groups,  comet-,  487. 

GUYOT,  A.  (1807-84),  Swiss- American 
geologist,  339. 

Gyroscope,  the,  showing  rotation  of 
earth,  127 ;  illustrating  cause  of  pre- 
cession, 168. 


600 


MANUAL   OF   ASTRONOMY 


H  and  K  lines  of  calcium,  reversed  in 
solar  prominences,  sun-spots,  and 
faculous  regions  of  solar  surface,  253, 
257. 

Habitability  of  Mars,  417. 

HALE,  G.  E.  (1808 ),  director  of  Car- 
negie Solar  Observatory,  222,  261. 

HALL,  A.  (1829-1907),  Prof.  U.  S.  N.,  416, 
445. 

HALLEY,  E.  (1656-1722),  second  Astrono- 
mer Royal,  405,  470,  484,  537. 

HARDING,  C.  (1765-1834),  German  astr., 
418. 

HARKNESS,  W.  (1837-1903),  Prof.  U.  S.N., 
475. 

Harmonic  law,  Kepler's,  307,  308. 

HARRISON,  J.  (1693-1766),  English  horol- 
oger,  55. 

Harvard  Observatory  photographs,  of 
asteroids,  419;  of  Eros,  428;  discov- 
ery of  Saturn's  dusky  ring  and  eighth 
satellite,  447,  452;  Harvard  photom- 
etry, the,  560;  catalogues  of  stellar 
spectra,  572. 

Harvest  and  hunter's  moon,  194. 

Heat,  solar,  267-275:  its  quantity,  267- 
271 ;  the  solar  constant,  267 ;  method 
of  measurement,  268;  absorption  by 
earth's  atmosphere,  268;  in  terms  of 
melting  ice,  269,  271 ;  expressed  as 
energy,  270,  271 ;  its  intensity  (tem- 
perature), 272,  273;  its  constancy, 
274 ;  its  maintenance,  275,  276 :  from 
Jupiter  and  Saturn,  563 ;  stellar,  563 ; 
theory  of,  conclusions  from  it  as  to 
age  and  duration  of  system,  617. 

HEIS,  E.  (1806-77),  German  astr.,  532, 
557. 

Heliocentric  place  of  a  planet,  368. 

Heliograph,  the,  232. 

Heliometer,  the,  72 ;  used  for  solar  par- 
allax, 467,  468,  472 ;  for  stellar  paral- 
lax, 551. 

Helioscopes,  or  solar  eyepieces,  231. 

Helium,  in  sun,  250,  257;  discovery  of, 
257 ;  in  stars,  576 ;  in  nebulae,  603. 

HELMHOLTZ,  H.  (1828-94),  German  physi- 
cist, 275. 

HENCKE,  L.  (1793-1866),  German  ama- 
teur, 418. 

HENDERSON,  T.  (1798-1844),  first  direc- 
tor of  Cape  of  Good  Hope  Observa- 
tory, 548,  549. 

HENRY  BROTHERS,  Paul  (1848-1905)  and 
Prosper  (1849-1903),  photograph«rs  of 
Paris  Observatory,  536. 

HERSCHEL,  A.  S.  (1836-1907),  English 
astr.  (son  of  Sir  John),  526. 

HERSCHEL,  SIR  JOHN  (1792-1871),  Eng- 
lish astr.  (son  of  Sir  William),  231, 
242,  267,  389,  452,  456,  557,  606. 


HERSCHEL,   SIR  WILLIAM    (1738-1822), 

English  astr.,  452,  453,  456,  543,  555, 

586,  606. 
HEVELIUS,    J.    (1611-87),    Polish    astr., 

481. 
HIPPARCHUS  (125  B.C.),  Greek  astr.,  161, 

165,  464,  532,  533,  555;  lunar  crater, 

221. 
HOLDEN,  E.  S.  (1846 ),  first  director 

of  Lick  Observatory,  504,  601. 
HOLMES,  E.  (? ),  English  amateur, 

—  his  comet  of  1892,  479,  493,  498. 
HOOKE,  R.    (1635-1703),  English   astr., 

410. 
Horizon,  the,  defined,  12, 13;  dip  of,  13, 

77. 

Horizon,  artificial,  74. 
HOUGH,  G.  W.  (1836-1909),   director  of 

Dearborn  Observatory,  59,  434. 
Hour  angle  defined,  21,  29. 
Hour-circle  defined,  20. 
HUGGINS,   SIR  W.   (1824-1910),   English 

spectroscopist,  258,  393,  409,  504,  541, 

563,  567,  570,  575,  602. 
HULL,  G.  F.  (1870 ),  American  physi- 
cist, 502. 

HUMBOLDT,  A.  (1769-1859),  German  nat- 
uralist, 387. 
HUMPHREYS,  W.  J.  (? ),  American 

physicist,  256,  542. 
Hunter's  moon,  194. 
HUSSEY,  W.  J.  (? ),  American  astr., 

504. 


HUTCHINS,   C.   C.    (?- 
physicist,  211. 


-),   American 


HUYGHENS,  C.  (1629-95),  Dutch  physi- 
cist, 44,  55,  410,  447,  452. 

Hydrocarbons  in  comets,  498. 

Hydrogen,  in  sun,  250 ;  in  sun-spots,  253 ; 
in  chromosphere  and  prominences, 
257;  in  stellar  spectra,  568;  in  tem- 
porary stars,  575 ;  in  nebulae,  602. 

Hyperbola,  the,  314,  315,  320,  482. 

Hyperion,  satellite  of  Saturn,  386,  452. 

I 

lapetus,  outer  satellite  of  Saturn,  386, 
449,  452. 

Illusion,  optical,  apparently  enlarging 
celestial  objects  near  the  horizon,  9. 

Inclination  of  planetary  orbits  oscillates 
slightly  under  perturbation,  376. 

Inferior  planets,  their  apparent  oscilla- 
tion on  each  side  of  the  sun,  358. 

Instantaneous  ellipse,  the,  324. 

Interior  of  earth,  its  probable  condition, 
154. 

Interpolation  of  observations,  367. 

Intramercurial  planets,  429. 

Invariable  plane,  the,  378. 

Inverse  problem  of  motion  under  gravita- 
tion, 313-321. 


INDEX 


601 


Iris,  an  asteroid,  468. 

Iron,  in  the  sun,  250;  in  comet  of  1882, 

498;  in  meteorites,  508;  in  stars,  507. 
Irregular  variations  of  light  in  comets, 

497;  in  stars,  574  (2). 


JANSSEN,  J.  (1824-1907),  French  spectro- 
scopist,  258,  409. 

Jena,  new  kinds  of  optical  glass,  45. 

JEWELL,  L.  E.  (? ),  American 

physicist,  photograph  of  solar  spec- 
trum, 246. 

Julian  calendar,  the,  184. 

Julian  period  and  epoch,  188. 

JULIUS,  W.  H.  (? ),  Dutch  physi- 
cist, 256. 

Juno,  an  asteroid,  discovery  of,  418; 
diameter,  422. 

Jupiter,  387,  389,  431-442:  orbit,  period, 
etc.,  431;  diameter,  mass,  etc.,  432; 
telescopic  appearance,  433;  atmos- 
phere and  spectrum,  434;  rotation, 
435 ;  physical  condition  and  red  spot, 
436 ;  probable  temperature,  437 ;  satel- 
lites, 438, 439 ;  eclipses  and  transits  of 
satellites,  439,  441 ;  determination  of 
the  constant  of  the  light-equation,  and 
the  distance  of  the  sun  from  eclipses 
of  the  satellites,  441,  442 ;  his  relations 
to  comets,  484,  485,  494;  heat  from 
Jupiter,  563. 


KANT,  IMMANUEL  (1724-1804),  German 

philosopher.  613. 
KAPTEYN,  J.  C.  (? ),  Dutch  astr., 

554,  577,  page  587. 

KEELER,  J.  E.   (1857-1900),  second  di- 
rector of  Lick  Observatory,  450,  541, 

542,  592,  599,  600,  602. 
KELVIN,  LORD  (Sir  William  Thomson) 

(1824-1907),  Scotch  physicist,  154,  512, 

513. 
KEPLER,  JOHN  (1571-1630),  German  astr., 

162,  163,  307,  418,  464,  481,  575,  577; 

lunar  crater,  219,  221. 
KIRCHHOFF,    G.    R.    (1824-87),  German 

physicist,  246,  247,  250,  252. 
KLEIN,  H.  (1842 ),  German  astr.,  531, 

note. 
KUSTNER  (? ),  German  astr.,  94. 


LADY  HUGGINS  cooperates  with  her  hus- 
band in  work  on  stellar  spectra,  570. 

Lagging  of  tides,  335. 

LAGRANGE,  J.  L.  (1736-1813),  French 
mathematician,  376. 

Lakes,  and  inland  seas,  tides  in,  344. 


LALANDE,  J.  (1732-1807),  French  astr., 
532. 

LANE,  J.  H.  (1819-80),  American  physi- 
cist, 276. 

LANGLEY,  S.  P.  (1834-1906) ,  American 
physicist,  212,  246,  266. 

LAPLACE,  P.  S.  (1749-1827),  French 
mathematician,  376,  386,  486,  613,  616. 

LASSELL,  W.  (1799-1880),  English  ama- 
teur, 456. 

Latitude,  celestial,  defined,  27,  29. 

Latitude,  solar,  of  sun-spots,  Spoerer's 
law,  241. 

Latitude,  terrestrial,  its  relation  to  posi- 
tion of  celestial  pole,  32 ;  astronomical, 
defined,  87,  138  (1) ;  determination  of, 
88-93 ;  determination  at  sea,  90,  112 ; 
variation  of,  94 ;  geocentric,  138  (3) ; 
geographical,  138  (2). 

Law,  of  gravitation,  143;  of  earth's 
orbital  motion,  162 ;  of  areas,  162, 303- 
306,  307 ;  Lane's,  of  gaseous  contrac- 
tion, 276;  Bode's,  349. 

Laws,  Kirchhoff' s,  relating  to  spectra. 
247;  Kepler's,  307. 

LEBEDEW,  P.  (? ),  Russian  physi- 
cist, 502. 

LEIBNITZ,  G.  (1646-1716),  German  philos- 
opher, lunar  mountains,  219. 

LEMONNIER,  P.  (1715-99),  French  astr., 
453,  457. 

Length  of  degrees  on  earth's  surface, 
formulae  for,  pages  581,  582. 

Leonids,  the,  521,  522,  525-527. 

LEVERRIER,  U.  J.  (1811-77),  French 
astr.,  423,  457,  472,  474,  526,  527,  page 
582. 

LEXELL,  J.  (1740-84),  453;  his  comet  of 
1770,  494. 

Librations  of  the  moon,  203;  of  Mer- 
cury, 394. 

Lick  Observatory  and  telescope,  51,  222, 
263,  409,  411,  422,  504,  542,  577,  592, 
599,  600,  602 ;  picture  of  observatory, 
page  476. 

Light,  aberration  of,  171,  173;  velocity 
of,  173;  of  the  moon,  210;  of  the  sun, 
265,  266;  the  equation  of,  440;  of 
comets,  497 ;  repulsive  force  of,  502 ; 
light  and  heat  of  meteors,  512;  re- 
ceived from  certain  stars,  562 ;  emitted 
by  certain  stars,  564. 

Light  curves  of  variable  stars,  579. 

Light-gathering  power  of  telescope,  43. 

Light-ratio  of  absolute  scale  of  star 
magnitudes,  557,  558. 

Light-year,  the,  547. 

Limits,  ecliptic,  lunar,  286 ;  solar,  293. 

Lines,  cotidal,  339,  340. 

Lines  in  spectrum,  explanation  of  dark, 
in  solar  spectrum,  247;  displacement 
of,  by  motion,  see  Doppler-Fizeau  prin- 
ciple. 


602 


MANUAL   OF    ASTRONOMY 


Local  and  standard  time,  110. 
LOCKYER,  SIR  J.  N.  (1836 ),  English 

spectroscopist,  242,  252,  258,  498,  528, 

569,  581,  592,  602,  603,  618,  note. 
Long  inequalities  of  planets,  375. 
Longitude,  celestial,  denned,  27,  29. 
Longitude,     terrestrial,     denned,     105; 

determination  of,  106-109 ;  at  sea,  107, 

108,  113,  114. 
LOWELL,  P.  (1855 ),  American  astr., 

394,  402,  403,  412,  413,  416,  417. 
Lunar,  distances,  108;  influences  on  the 

earth,  213;    photography,   218,    222; 

eclipses,  282-288 ;  perturbations,  326- 

329. 
LYMAN,  C.  S.  (1814-89),  American  astr., 

401. 
Lyras,  e,  457, 585,  597 ;  a  (Vega), 532, 558, 

560,  562,  563,  564. 


MAEDLER,  J.  H.  (1791-1874),  German 
astr.,  544,  609. 

Magnetism,  terrestrial,  disturbed  by 
moon,  213;  connected  with  sun-spots 
and  other  solar  disturbances,  243. 

Magnifying  power  of  telescope,  42. 

Magnitudes,  stellar,  555 ;  typical  stars  of 
first  and  second  magnitudes,  557 ;  dif- 
ference of,  its  relation  to  ratios  of 
brightness,  558 ;  of  Arcturus,  Capella, 
Jupiter,  Sirius,  Vega,  and  the  Sun, 
558;  visible  with  telescopes  of  given 
aperture,  559. 

Maintenance  of  solar  heat,  275. 

Maps,  of  the  moon,  218;  of  planetary 
orbits,  351 ;  of  Mars,  414 ;  of  stars, 
532,  note. 

Marine  method  of  determining,  latitude, 
90,112;  time,  103;  longitude,  107, 108 ; 
Sumner's  method  giving  both  latitude 
and  longitude,  113,  114. 

Mars,  407-417 ;  orbital  data,  407 ;  dimen- 
sions, mass,  density,  surface  gravity, 
etc.,  408;  telescopic  aspect,  phase, 
albedo,  and  atmosphere,  409 ;  rotation, 
410;  topography,  411;  canals  and 
their  gemination,  412,  413;  seasonal 
changes,  413 ;  maps,  414 ;  temperature, 
415 ;  satellites,  416 ;  habitability,  417 ; 
observed  for  solar  parallax,  466,  467. 

MASKELYNE,  N.  (1732-1811),  fourth  As- 
tronomer Royal ;  lunar  crater,  221. 

Mass,  definition  of,  and  distinction  from 
weight,  140, 141 ;  of  earth  determined, 
148-153;  of  moon,  200;  of  sun,  225 ;  of 
planet,  how  determined,  380-382;  of 
comets,  494,  of  shooting-stars,  519; 
of  binary  systems,  594.  For  masses 
of  planets,  see  Table  I,  page  583. 

MAXWELL,  J.  CLERK  (1831-79),  English 
physicist,  502. 


Mazapil  meteorite,  the,  524. 

Mean  solar  time  defined,  98,  174. 

Mediterranean,  tides  in,  344. 

MELLONI,  M.  (1798-1854),  Italian  physi- 
cist, 211. 

Mercury,  390-396;  orbital  data,  391; 
dimensions,  mass,  density,  and  surface 
gravity,  392;  telescopic  appearance, 
phases,  and  atmosphere,  393 ;  rotation 
and  librations,  394;  albedo,  395; 
transits,  396. 

Meridian,  celestial,  defined,  14,  20;  ad- 
vantage of  observations  on,  60. 

Meridian  or  transit  circle,  the,  68,  69; 
use  in  determining  latitude,  89 ;  places 
of  heavenly  bodies,  116,  534,  535. 

Meridian,  terrestrial,  measurement  of 
arc  of,  121,  122,  133. 

MESSIER,  C.  (1730-1817),  French  astr., 
479,584,599;  lunar  crater,  221. 

Metallic  prominences,  260 ;  lines  in  spec- 
trum of  comet,  498. 

Meteoritic  hypothesis,  528,  603. 

Meteors,  meteorites,  and  shooting-stars, 
507-528;  meteorites  (aerolitic),  fall  of, 
507 ;  weight,  relative  number  of  stones 
and  irons,  and  number  in  cabinets, 
508 ;  appearance  and  chemical  consti- 
tution, 509;  path  and  velocity,  510; 
method  of  observation,  511 ;  explana- 
tion of  light  and  heat,  512;  their 
origin,  513;  probable  total  annual 
number,  514.  For  silent  meteors 
(shooting-stars)  and  meteoric  show- 
ers, see  Shooting-Stars  and  Showers. 

Meton  (433  B.C.  ?),  Greek  astr.,  187. 

Metonic  cycle,  187. 

MICHELL,  REV.  J.  (? 1793),  English 

astr.,  148. 

MICHELSON,  A.  A.  (1852 ),  American 

physicist,  173,  256. 

Micrometer,  filar,  the,  71,  117,  379,  551, 
585. 

Midnight  sun,  the,  36. 

Milky  Way,  the,  605,  606. 

Mimas,  innermost  satellite  of  Saturn,  452. 

MINCHIN,  G.  M.  (? ),  English  physi- 
cist, 560. 

Mira  (o  Ceti),  remarkable  variable,  578, 
581. 

Missing  stars,  574. 

MOHLER,  J.  F.  (? ),  American 

physicist,  256,  542. 

Monoceros,  remarkable  nebula  in,  600. 

Month,  sidereal  and  synodic,  191 ;  nodical 
ordraconitic,  192;  lengthened  by  sun's 
disturbing  action,  327;  various  kinds, 
length  of,  page  582. 

Moon,  the,  Chapter  VII,  189-222 ;  appar- 
ent motion  and  definitions  of  terms, 
190 ;  sidereal  and  synodic  months,  191 ; 
the  moon's  path,  nodes,  and  nodical 
month,  192 ;  interval  between  transits, 


INDEX 


603 


193 ;  harvest  and  hunter's  moon,  194 ; 
form  of  orbit,  195 ;  distance,  parallax, 
and  velocity,  196,  197 ;  orbit  with  ref- 
erence to  sun,  198 ;  diameter,  etc.,  199 ; 
mass,  200 ;  density  and  surface  grav- 
ity, 201;  rotation,  202;  librations, 
203 ;  phases,  204,  205 ;  earth-shine  on 
moon,  206;  atmosphere,  207-209;  ab- 
sence of  water,  208 ;  light  and  albedo, 
210;  heat  and  temperature,  211,  212; 
influences  on  earth,  213;  telescopic 
appearance,  214 ;  surface  formations, 
215-217;  maps,  218,  221;  nomencla- 
ture, 219;  supposed  changes,  220; 
photographs,  222.  For  tabulated  data, 
see  also  Table  II,  page  584. 

Moon  (topics  not  treated  in  Chapter  VII), 
longitude  by  observations  of,  108; 
eclipses  of,  282-288 ;  heat  radiation  as 
affected  by  eclipse,  287 ;  parabolic 
velocity  at  her  surface,  319;  pertur- 
bations of,  326-329;  her  tide-raising 
force,  332-334 ;  effect  of  tides  upon  her 
motion,  346;  projection  and  calcula- 
tion of  eclipses,  703,  704. 

Mountains,  lunar,  216. 

Motion,  free,  301 ;  of  body  acted  on  by 
force,  302-306;  apparent,  of  planets, 
353-358;  of  planets  in  space  relative 
to  earth,  354;  relative,  law  of,  354, 
546;  in  right  ascension,  355;  in  lati- 
tude, 356;  in  elongation  from  sun, 
357,  358;  orbital,  of  earth,  point 
to  which  directed,  516;  of  stars, 
common  and  proper,  537-539;  real, 
of  stars,  540-542;  of  sun  in  space, 
543. 

Motion  in  line  of  sight,  see  Radial  velocity. 

MULLER,  G.  (? ),  German  astr., 

422,  560  (2). 

Multiple  stars,  597. 


Nadir,  the,  denned,  11. 

Nadir  point  of  meridian-circle,  69. 

Naked-eye  stars,  number  of  each  magni- 
tude, 556. 

NASMYTH,  J.  (1808-90) ,  English  amateur, 
215. 

Neap  tides  denned,  331. 

Nearness  of  a  star,  indications  of  it, 
552. 

Nebula  and  nebulse;  radial  motion  of, 
541,  602 ;  temporary  star  transformed 
into,  576,  577 ;  surrounding  Nova 
Persei,  577;  naked-eye  nebula,  and 
various  forms  of,  599 ;  number  of,  599 ; 
supposed  changes,  601 ;  spectrum  of, 
602 ;  nature  of,  603 ;  distance  and  dis- 
tribution, 604. 

Nebular  hypothesis,  the,  613;  difficulties 
and  necessary  modifications,  614. 


NEISON,  E.   N.  (? 


)    (since    1888, 


(si 

NEVILLE,  E.  N.),  English  astr.,  197, 
221,  page  582. 

Negative  conclusions  as  to  presence  of 
elements  in  heavenly  bodies  unwar- 
ranted, 251,  498,  603. 

Negative  parallax,  551  ;  magnitudes,  558. 

Neptune,  457-461  ;  discovery,  457  ;  error 
of  predicted  orbit,  458;  orbital  data, 
459  ;  diameter,  mass,  etc.,  459  ;  satellite, 
460;  the  sun  as  seen  from  Neptune, 
461  ;  his  family  of  comets,  485. 

NEWALL,  H.  F.  (?  -  ),  English  astr., 
592. 

NEWCOMB,  S.  (1835-1909),  Prof.  U.  S.  N., 
240,  474,  475,  note,  556,  562,  note,  608, 
617. 

NEWTON,  H.  A.  (1830-96),  American 
astr.,  489,  496,  513,  516,  525,  526. 

NEWTON,  SIR  ISAAC  (1642-1727),  English 
philosopher,  49,  74,  122,  168,  308,  309, 
311,  312,  313,  316,  317,  481. 

Newtonian  telescope,  49;  constant,  145, 
150. 

NICHOLS,  E.  F.  (1869  -  ),  American 
physicist,  502,  563. 

Nickel,  in  sun,  250;  in  meteoric  iron, 
508. 

Nicol  prisms  in  photometry,  560  (2). 

Nodes,  defined,  192  ;  of  moon's  orbit  and 
•  their  regression,  192,  327  (3)  ;  revolu- 
tion of,  in  planetary  orbits,  376. 

NORDENSKIOLD,  A.  E.  VON  (1832-1901), 
Swedish  explorer,  518. 

Novae,  or  temporary  stars,  575-577. 

Nucleus,  or  umbra,  of  sun-spot,  234; 
of  the  sun,  277;  of  a  comet,  492, 
493. 

Number,  yearly,  of  eclipses,  297;  in  a 
Saros,  299  ;  of  asteroids,  418,  424  ;  an- 
nual, of  aerolites,  514;  hourly  and 
daily,  of  shooting-stars,  516;  of  the 
stars,  530  ;  of  visible  stars  of  different 
magnitudes,  556;  of  variable  stars, 
583;  of  known  (telescopic)  binaries, 
587;  of  spectroscopic  binaries,  592, 
593;  of  nebulae,  599,  602. 

Nutation,  170  ;  constant  of  (Paris  Confer- 
ence), page  582. 


Oberon,  outermost  satellite  of  Uranus, 
456. 

Object-glass,  light-gathering  power,  43; 
different  forms  of,  44 ;  secondary  spec- 
trum of,  45;  aplanatic,  45;  diameter 
required  to  show  stars  of  given  mag- 
nitude, 559. 

Oblateness,  or  ellipticity,  of  the  earth, 
132,  134,  136,  page  581.  For  oblate- 
ness  of  planets,  see  Table  I,  page  583. 

Oblique  sphere,  the,  35. 


604 


MANUAL    OF   ASTRONOMY 


Obliquity  of  the  ecliptic,  defined,  156; 
change  of,  164  (3) ;  ancient  observa- 
tion of,  164,  note;  element  in  equa- 
tion of  time,  176 ;  its  value,  page  582. 

Observations,  interpolation  of,  367. 

Occultation,  circle  of  perpetual,  35 ;  lon- 
gitude determined  by,  108;  of  stars, 
300. 

Oculars,  or  eyepieces,  47. 

OLBEBS,  H.  W.  M.  (1758-1840),  German 
amateur,  418. 

OLMSTED,  D.  (1791-1859),  American 
physicist,  525. 

Omicron  Ceti,  see  Mira. 

Ophiuchi,  Nova,  575. 

OPPOL,ZER,E.  (1869-1907),  Austrian  mete- 
orologist, 242. 

OPPOLZER,  TH.  VON  (1841-86),  Austrian 
astr.,  296,  526. 

Opposition  defined,  190,  352. 

Optically  double  stars,  586. 

Orbit,  of  the  earth,  158-161 ;  changes  in, 
164 ;  of  moon,  195-198 ;  curvature  of, 
226;  of  a  planet,  the  elements,  362; 
parallactic  of  a  star,  546. 

Orbital  data  for  the  planets,  Table  I, 
page  583 ;  for  the  satellites,  Table  II, 
pages  584, 585.  See  also  under  names 
of  individual  planets. 

Orbits,  of  comets,  481-488;  of  binary 
stars,  587-590,  Table  VII,  page  590; 
apparent  and  real,  588 ;  relative  and 
absolute,  589 ;  their  size,  590. 

Orbits  in  the  system  of  the  stars,  ques- 
tion of,  610. 

Origin,  of  the  asteroid  group,  425;  of 
comet-families,  485 ;  of  comets,  489 ; 
of  aerolitic  meteors,  513. 

Orion,  great  nebula  of,  599,  600,  602. 

Oscillations,  of  eccentricity  and  inclina- 
tion of  planetary  orbits,  164,  376; 
free  and  forced,  338. 


Pallas,  asteroid,  discovery  of,  418 ;  incli- 
nation, 421 ;  diameter,  422. 

Parabola,  the,  314,  315. 

Parabolic,  elliptic,  and  hyperbolic  orbits 
of  comets,  their  relative  number,  482. 

Parabolic  orbits  of  comets,  481-483. 

Parabolic  velocity,  the  (or  velocity  from 
infinity),  defined,  318;  at  the  surface 
of  different  bodies,  319;  relation  be- 
tween it  and  the  species  of  the  orbit 
described  by  a  body,  320 ;  determina- 
tion of  its  value  at  distance  unity,  320. 

Parallactic  inequality  of  the  moon  and 
its  use  to  determine  the  solar  paral- 
lax, 473. 

Parallax,  geocentric,  or  diurnal,  defined, 
78;  its  law,  79;  relation  to  distance, 
79;  equatorial,  80;  of  the  moon  deter- 


mined, 196,  197 ;  of  the  sun,  223 ;  also 
Chapter  XV,  463-475 ;  importance  and 
difficulty  of  problem,  463 ;  historical, 
464;  geometrical  methods,  observa- 
tions of  Mars  and  of  asteroids,  466- 
468 ;  transits  of  Venus,  469-472 ;  gravi- 
tational methods,  473,  474;  table  of 
values  obtained  by  different  methods, 
475;  value  adopted  by  Paris  Con- 
ference, page  582. 

Parallax,  heliocentric  or  annual,  defined, 
78,  544;  of  stars,  545-554;  its  deter- 
mination, by  the  absolute  method, 
549 ;  by  the  differential  method,  550, 
551 ;  negative  parallax,  551 ;  possible 
spectroscopic  method,  553;  stellar 
parallaxes,  Table  IV,  page  587. 

Parallel  lines,  their  vanishing  point,  7. 

Paris  Conference  of  1896  adopted  values 
of  astronomical  constants,  page  582. 

Paris  Observatory,  its  photographic  tele- 
scope, 536;  engraving  of  the  observa- 
tory, page  536. 

Partial  eclipses,  of  moon,  284 ;  of  sun,  291. 

Paths  of  meteors,  510,  517. 

PEIRCE,  B.  (1809-80),  American  mathe- 
matician, 449,  489. 

Pendulum,  compensation,  55 ;  Foucault's, 
125 ;  use  in  determining  the  figure  of 
the  earth,  136. 

Penetrating  power  of  solar  rays,  273. 

Penumbra  of  sun-spots,  234,  235;  of 
earth's  shadow,  283;  of  moon's 
shadow,  291. 

Perigee  defined,  195. 

Perihelia  and  nodes  of  planetary  orbits, 
their  revolution,  164,  376. 

Perihelion,  defined,  160;  distances  of 
comets,  488. 

Period  of  a  planet,  expression  for,  321 ; 
methods  of  determining,  369,  370. 

Periodic  perturbations  of  the  earth,  164 ; 
of  the  planets,  375. 

Periodic  variables,  578-580. 

Periodicity  of  sun-spots,  240. 

Periods  of  planets,  sidereal  and  synodic, 
and  relation  between  them,  351 ; 
unchangeable  by  secular  perturba- 
tions, 376. 

Permanent  tides,  condition  for,  336. 

Perpetual  apparition,  circle  of,  35. 

PERROTIN,  J.  (1845-1904),  French  astr., 
173,  403. 

Perseids,  the,  522,  526. 

Personal  equation,  64. 

Perturbations,  of  the  earth's  orbit,  164 ; 
of  the  moon,  326-329;  of  the  planets, 
374-377 ;  mass  of  planet  determined 
by  means  of,  380 ;  of  Uranus  leading 
to  discovery  of  Neptune,  457 ;  of 
Venus,  Mars,  and  Eros  used  to  deter- 
mine solar  parallax,  474;  of  the 
Leonid  meteors,  525. 


INDEX 


605 


Phase  and  phases,  of  the  moon,  204, 
205 ;  of  Mercury,  393 ;  of  Venus,  399 ; 
of  Mars,  409;  of  Jupiter,  433;  of 
Saturn's  ring,  448. 

Phobos,  inner  satellite  of  Mars,  416. 

Phoebe,  the  ninth  satellite  of  Saturn, 
452. 

Photochronograph,  the,  65. 

Photographic  telescopes  and  star-chart 
campaign,  536. 

Photographs,  of  star  trails,  18;  of  moon, 
222 ;  of  sun,  232 ;  of  sun-spots,  235 ; 
of  solar  spectrum,  246,  249;  of  flash 
spectrum,  252 ;  of  solar  prominences, 
261 ;  of  the  corona  and  its  spectrum, 
262,  263;  discovery  of  asteroids  by, 
419;  of  comets,  479,  504;  of  stars, 
536 ;  of  stellar  spectra,  542,  570,  571, 
591,  593;  of  nebula  around  Nova 
Persei,  577 ;  of  star  clusters,  584,  598 ; 
of  nebulse,  599,  600;  of  the  Milky 
Way,  605. 

Photography,  applied  to  observations  of 
star  transits,  65;  to  determination 
of  place  of  a  celestial  object,  117 ;  to 
discovery  of  asteroids,  419 ;  to  obser- 
vation of  eclipses  of  Jupiter's  satel- 
lites, 441 ;  to  transits  of  Venus,  472 ;  to 
discovery  of  comets,  479;  to  star 
charting,  536 ;  to  stellar  spectra,  542, 
570,  572,  591,  593. 

Photosphere,  the,  233,  278. 

Physical  methods  of  determining  the 
sun's  distance  by  means  of  the  veloc- 
ity of  light,  173,  442,  475. 

PIAZZI,  G.  (1746-1826),  Sicilian  astr.,418. 

PICABD,  J.  (1620-82),  French  astr.,  122, 
312. 

PICKERING,  E.  C.  (1846 ),  fourth  direc- 
tor of  Harvard  College  Observatory, 
383,  416,  441,  560  (2),  569,  571,  584, 
593,  600. 

PICKERING,  W.  H.  (1858 ),  452. 

Place  of  a  heavenly  body  denned,  8. 

Plane,  invariable,  378 ;  galactic,  605. 

Planet,  methods  of  determining  its 
period,  369,  370;  geometrical  method 
of  determining  its  distance  from  the 
sun,  371-373 ;  determination  of  diam- 
eter, surface,  and  volume,  379;  of 
mass,  density,  and  surface  gravity, 
380;  of  its  rotation,  383;  of  albedo, 
384;  of  surface  markings,  385. 

Planetary  orbits,  map  of,  351 ;  elements 
of,  362,  363 ;  general  method  of  deter- 
mining elements,  365;  perturbations, 
374-376;  data,  relative  accuracy  of, 
388 ;  data,  Table  I,  page  583. 

Planetary  system,  stability  of,  377;  its 
genesis,  612-615. 

Planetesimal  hypothesis,  615. 

Planets,  list  of,  347,  348 ;  Bode's  law  of 
distances,  349,  350 ;  periods,  351 ;  ap- 


parent motions  of,  353,  358;  classifi- 
cation of,  387 ;  intramercurial,  429 ; 
possible,  attending  stars,  596;  data 
relating  to  them,  Table  I,  page  583. 

PLATO  (429-348  B.C.),  Greek  philosopher ; 
lunar  crater,  219,  221. 

Pleiades,  the,  544,  598 ;  nebula  in,  600. 

PLINY,  C.,  the  elder  (A.D.  23-79),  Roman 
naturalist,  274 ;  lunar  crater,  221. 

POGSON,  N.  (1829-91),  English  astr.,  557. 

Point  in  heavens  towards  which  earth  is 
moving  at  any  moment,  516 ;  towards 
which  sun's  motion  in  space  is 
directed,  543. 

Polar  caps,  of  Venus,  402 ;  of  Mars,  411. 

Polaris  (a  Ursae  Minoris),  the  pole-star, 
18;  spectrum  of,  compared  with  tita- 
nium, 542 ;  a  typical  second-magnitude 
star  (nearly),  557;  a  spectroscopic 
binary,  592. 

Pole,  celestial,  defined,  19;  relation 
between  its  altitude  and  the  observer's 
latitude,  32 ;  its  precessional  motion, 
166. 

Pole,  of  the  ecliptic,  defined,  27,  156;  its 
position  in  heavens,  156 ;  of  the  sun, 
229;  of  the  Galaxy,  or  Milky  Way, 
605. 

Pole,  terrestrial,  its  wandering,  94. 

PONS,  J.  L.  (1761-1831),  French  astr.,  479. 

Position,  circle  of,  of  Sumner's  method, 
113. 

Position  micrometer,  71 ;  angle,  585. 

Potsdam  Astrophysical  Observatory,  its 
photographic  telescope,  Frontispiece ; 
spectrograph,  542;  photometric  star- 
catalogue,  560  (2) ;  engraving  of  the 
observatory,  page  454. 

POUILLET,  C.  S.  (1791-1868),  French 
physicist,  267,  272. 

Poundal,  the,  142. 

Power,  magnifying,  of  telescope,  42; 
light-gathering,  43. 

Precession  of  the  equinoxes,  discovery 
of,  165 ;  effect  on  position  of  celestial 
pole,  166 ;  on  signs  of  zodiac  and  on 
visibility  of  constellations,  167;  its 
physical  cause,  168 ;  constant  of  (Paris 
Conference),  page  582. 

Pressure,  its  effect  in  shifting  lines  of 
spectrum,  256,  542. 

Prime  vertical,  defined,  14 ;  instrument, 
66. 

Priming  of  the  tides,  331. 

Printing  chronograph,  59. 

Prismatic  camera,  252,  263. 

PRITCHARD,  REV.  C.  (1808-93),  English 
astr.,  551,  560. 

Problem,  Kepler's,  163;  of  two  bodies, 
316,  317 ;  of  three  bodies,  322-325. 

Progressive  changes  of  brightness  in 
stars,  574  (1). 

Projectile  force,  301. 


606 


MANUAL   OF   ASTRONOMY 


Projectiles,  deviation  of,  by  earth's  rota- 
tion, 127. 

Projection  of  a  lunar  eclipse,  703. 

Prominences,  solar,  257,  279 ;  their  obser- 
vation by  means  of  the  spectroscope, 
258,  259;  different  classes,  260;  pho- 
tography of,  261. 

Proper  motion  of  stars,  discovery  of,  537 ; 
how  detected,  538;  average,  for  stars 
of  different  magnitudes  and  maxi- 
mum, 539;  large,  best  a  priori  indi- 
cation of  nearness,  552. 

PTOLEMY,  CLAUDIUS  (A.D.  140),  Alexan- 
drian astr.,  359,  399,  464,  481,  531, 532, 
533,  555;  lunar  crater,  221. 

Punctual  variables,  581. 

PURBACH,  G.  (1423-61),  German  astr.; 
lunar  crater,  221. 


Quadrature  defined,  190,  352. 
Quantity  of  solar  heat,  267-270. 
Quartz,  fiber  for  torsion-balance,   153; 
prisms,  570. 

R 

Radial  velocity  (in  line  of  sight),  deter- 
mined by  Doppler-Fizeau  principle, 
254,  255 ;  of  stars,  541,  542,  543,  Table 
V,  page  588 ;  of  nebulae,  602. 

Radian,  the,  defined,  and  its  value  in 
seconds  of  arc,  9. 

Radiant,  the,  of  meteoric  showers,  521 ; 
stationary,  523. 

Radiation,  lunar,  211,  287 ;  solar,  267-275 ; 
Stefan's  Law  of,  272. 

Radius  vector  defined,  160. 

RAMSAY,  W.  (1852 ),  English  chemist, 

257. 

RAMSDEN,  J.  (1735-1800),  English  mech- 
anician, 47,  69. 

Rate  of  clock  defined,  56. 

Ray  systems  on  moon,  217. 

Recurrence,  of  eclipses,  299;  of  transits 
of  Mercury,  396 ;  of  transits  of  Venus, 
406. 

Red  spot  of  Jupiter,  436. 

Reflecting  telescope,  49,  577,  600. 

Refracting  telescope,  simple,  41 ;  achro- 
matic, 44. 

Refraction,  astronomical,  82,  83,  Table 
VIII,  page  491 ;  anomalous,  256. 

Regression,  of  nodes  of  moon's  orbit,  192, 
327 ;  of  planetary  orbits,  376. 

REICHENBACH,  C.  VON  (1788-1869),  Ger- 
man chemist,  514. 

Relative  motion,  law  of,  354,  546. 

Repulsive  force  of  sun,  502. 

Reticle,  the,  48. 

Retrograde  motion,  of  planets,  355;  of 
satellites  of  Uranus,  456 ;  of  Neptune, 
460. 


Reversal  of  spectrum  lines,  247. 

Reversing  layer,  the,  252,  279. 

Rhea,  satellite  of  Saturn,  452. 

RICCIOLI,  G.  B.  (1598-1671),  Italian  astr., 
219. 

Right  ascension  defined,  24,  26. 

Right  ascension  and  declination,  deter- 
mined by  the  meridian-circle,  116, 
534 ;  conversion  into  azimuth  and  alti- 
tude, 701;  into  (celestial)  longitude 
and  latitude,  702. 

Right  sphere,  the,  33. 

Rings  of  Saturn,  447-451. 

RITCHEY,  G.  W.  (? ),  American 

mechanician,  222. 

Rivers,  tides  in,  341. 

ROBERTS,  A.  (? ),  South  African 

astr.,  594. 

ROBERTS,  I.  (1829-1904),  English  ama- 
teur, 600,  601. 

ROEMER  O.  (1644-1710),  Danish  astr., 
440.  ' 

Rordame's  comet  of  1893,  477,  504. 

ROSSE,  LORD  (third  earl)  (1800-67).  Eng- 
lish amateur,  51. 

ROSSE,  LORD  (fourth  earl)  (1840-1908), 
211,  212,  287. 

Rotation,  apparent,  of  celestial  sphere, 
18;  of  earth,  proofs,  124-127;  possi- 
ble variations  in  its  rate,  128,  345,  396 ; 
of  the  moon,  202 ;  of  the  sun,  229, 230 ; 
of  planets,  how  determined,  383;  of 
Mercury,  394 ;  of  Venus,  403 ;  of  Mars, 
410 ;  of  Jupiter,  435 ;  of  Saturn,  445, 
450;  of  Saturn's  rings,  450. 

ROWLAND,  H.  A.  (1848-1901),  American 
physicist,  250. 

Runaway  star,  the,  539. 

RUNGE,  C.  (? ),  German  spectro- 

scopist,  250. 

RUSSELL,  H.  N.  (1877 ),  American 

astr.,  401,  594. 

RUTHERFURD,  L.  M.  (1816-92),  Ameri- 
can amateur,  222. 


Sappho,  an  asteroid  observed  for  paral- 
lax, 468. 

Saros,  the,  299. 

Satellite  and  satellites,  mass  of  a  planet 
determined  by  means  of  its,  380-382 ; 
satellite  systems,  data  determined, 
386;  hypothetical,  of  Venus,  405;  of 
Mars,  416,  613 ;  of  Jupiter,  438^42 ;  of 
Saturn,  452 ;  of  Uranus,  456 ;  of  Nep- 
tune, 460 ;  data,  Table  II,  page  584. 

Saturn,  443-452 ;  orbital  data,  444 ;  dimen- 
sions, mass,  density,  rotation,  etc., 
445;  surface  features,  albedo,  and 
spectrum,  446;  rings,  discovery,  ap- 
pearance and  dimensions,  447 ;  their 
phases,  448;  their  nature,  449; 


INDEX 


607 


Keeler's  spectroscopic  demonstration 
of  their  non-coherent  structure,  450; 
their  stability,  451 ;  the  satellites,  452 ; 
heat  from  Saturn,  563 ;  rings  suggest 
nebular  hypothesis,  613. 

Scale,  absolute,  of  stellar  magnitude,  557. 

SCALIGER,  JOSEPH  (1540-1609),  French 
chronologer,  188. 

SCHAEBERLE,  J.  M.  (1853 ),  American 

astr.,  257. 

SCHEINER,  J.  (? ),  German  astr., 

255,  267. 

SCHIAPARELLI,  G.  V.  (1835-1910) ,  Italian 
astr.,  394,  403,  412,  414,  526. 

SCHMIDT,  A.  (? ),  German  astr., 

278. 

SCHMIDT,  J.  (1825-84),  director  of  Obser- 
vatory of  Athens,  218,  575. 

SCHOENFELD,  E.  (1828-91),  533. 

SCHREIBERS,  C.  VON  (1775-1852),  German 
amateur,  514. 

SCHROTER,  J.  H.  (1745-1816),  394,  402. 

SCHWABE,  S.  H.  (1789-1875),  German 
astr.,  240. 

Scintillation  of  stars,  84. 

Search  for  asteroids,  methods,  419 ;  for 
comets,  479. 

Seasons,  the,  178-181;  on  Mercury,  391; 
on  Mars,  412. 

SECCHI,  A.  (1818-78),  Italian  astr.,  234, 
237,  567,  568,  569. 

Secondary,  circles,  27,  29;  spectrum  of 
an  object-glass,  45. 

Secular,  acceleration  of  moon,  329 ;  per- 
turbations of  the  planets,  376. 

SEE,  T.  J.  J.  (1866 ),  Prof.  U.  S.  N., 

447,  455,  459,  516,  595,  Table  VII, 
page  590. 

SEELIGER,  H.  (? ),  German  astr., 

449. 

Semidiameter,  augmentation  of  moon's, 
81;  mean,  of  a  spheroid,  139,  432, 
page  581. 

SEXECA,  L.  A.  (4  B.C.-A.D.  65),  Roman 
philosopher,  481. 

Sextant,  the,  73-75. 

Shadow,  of  earth,  its  dimensions,  282, 
283,  285,  703,  704 ;  of  moon,  its  dimen- 
sions, 289;  its  velocity  over  earth's 
surface,  292. 

Shadow  bands  of  solar  eclipse,  294. 

Ship  at  sea,  determination  of  its  position, 
90,  107,  112,  113,  114. 

Shooting-stars,  515-520 ;  appearance, 
nature,  and  relation  to  aerolitic  mete- 
ors, 515;  their  number,  516;  path 
and  velocity,  517;  brightness,  ma- 
terial, trains,  518;  mass,  519;  their 
effects,  520. 

Shooting-star  showers,  see  Showers, 
meteoric. 

Short-period,  comets,  485, 486 ;  variables, 
581. 


Showers,  meteoric,  521-526 ;  the  radiant, 
521 ;  dates,  522 ;  stationary  radiants, 
523 ;  the  Mazapil  meteorite,  524 ;  con- 
nection with  comets,  525,  526. 

Sidereal,  day,  denned,  25;  time,  denned, 
25,  96;  relation  to  mean  solar  time, 
99;  sidereal  year,  the,  182;  sidereal 
and  synodic  periods,  and  equation 
expressing  relation  between  them, 
191,  351;  sidereal  year,  its  length, 
page  582. 

Siderostat,  the,  54. 

Signals,  artificial,  longitude  by,  109. 

Signs  of  the  zodiac,  157 ;  displacement  of, 
by  precession,  167. 

Sirius,  discovery  of  its  proper  motion, 
537 ;  radial  motion,  541 ;  its  light  com- 
pared with  sun's,  562, 564 ;  and  its  com- 
panion, relative  and  absolute  orbits, 
589 ;  its  parallax  and  mass,  590. 

Sixty-one  Cygni,  first  stellar  parallax, 
determined  by  Bessel,  548,  550. 

Slitless  spectroscope,  its  invention  and 
introduction,  571 ;  advantages  and 
disadvantages,  572 ;  use  for  spectro- 
scopic binaries,  593. 

Sodium  spectrum,  lines  of,  reversed,  247 ; 
in  sun,  250;  in  comets,  498. 

Solar  system,  see  System. 

Solar  (see  also  Sun),  time,  apparent  and 
mean,  97-99,  174;  eyepieces,  231; 
spectrum,  246 ;  prominences,  257-261 ; 
corona,  262-264;  constant,  267,  268: 
engine,  270;  eclipses,  289-296;  stars 
(second  class),  568. 

Solstices,  the,  23,  156. 

SOSIGENES  (50  B.C.),  Alexandrian  astr., 
184. 

Southern  cross,  once  visible  in  England, 
167. 

Spectrograph,  the,  542,  page  505. 

Spectrographic  determination  of  radial 
velocity,  542. 

Spectroheliograph,  the,  261. 

Spectroscope,  the,  described,  244;  the 
slitless,  571,  572. 

Spectroscopic,  determination  of  radial 
velocity,  254,  255,  541, 542 ;  method  of 
observing  solar  prominences,  259 ;  de- 
termination of  sun's  velocity  in  space, 
543;  method,  possible,  of  determin- 
ing parallax  of  binary  stars,  553; 
demonstration  possible  that  gravita- 
tion extends  to  the  stars,  587,  note ; 
binaries,  591-593. 

Spectrum  and  spectra,  secondary,  of 
object-glass,  45;  formation  of,  245; 
solar,  246;  lines,  reversal  of,  247; 
flash,  252;  of  sun-spots  and  faculae, 
253;  lines,  displacement  and  distor- 
tion of,  254-256 ;  of  prominences,  257 ; 
of  corona,  263;  of  Mercury,  393; 
Venus,  401,  403;  Mars,  409;  zodiacal 


608 


MANUAL   OF   ASTRONOMY 


light,  430 ;  Jupiter,  434 ;  Saturn,  446 ; 
Uranus,  455 ;  Neptune,  459 ;  of  comets, 
498;  of  shooting-stars,  518;  of  stars, 
541,  567-572,  576,  578 ;  of  nebulae,  602. 

Sphere,  celestial,  regarded  as  infinite,  7. 

Spheres,  attraction  of,  144. 

Spheroid,  mean  radius  of,  139,  432,  page 
581. 

Spiral  nebula?,  599. 

Spitzbergen,  supposed  meteoric  dust  in 
snow,  518. 

SPOERER,  G.  (1822-95),  German  astr., 
230,  241. 

Spring-tides  defined,  331. 

Spurious  disk  (telescopic)  of  star,  46. 

Stability  of  the  planetary  system,  377; 
of  Saturn's  rings,  451. 

Stagnation,  the  apparent  termination  of 
existing  tendencies,  618. 

Standard  time,  110. 

Star,  names,  532;  atlases,  532,  note; 
catalogues,  532,  533;  places,  their 
determination,  534;  mean  and  ap- 
parent, 535;  charts,  536;  motions, 
537-542;  spectra,  541,  567-572,  576- 
578;  parallax  and  distance,  545-553; 
magnitudes  and  brightness,  555^561 ; 
colors,  560;  clusters,  variables  in, 
584 ;  clusters,  598 ;  gauges,  Herschel's, 
606. 

Stars,  occultations  of,  300 ;  shooting,  515- 
520;  number  of,  visible,  556;  light 
from,  562,  564;  heat  from,  563;  miss- 
ing, 574  (1) ;  new  or  temporary,  575- 
577 ;  periodic  variable,  578-584 ;  dark, 
582, 589, 597 ;  double  and  binary,  585- 
595;  possible  planets  attending,  596; 
multiple,  597;  distribution  on  the 
celestial  sphere,  606;  in  space,  607, 
608 ;  system  of,  609,  610. 

Station  errors,  137. 

Stationary  points,  355 ;  radiants,  523. 

STEFAN  (? ),  German  physicist,  his 

law  of  radiation,  272. 

STEINHEIL,  R.  (?- ),*German  opti- 
cian, 47. 

Stellar,  parallax  defined,  545;  magni- 
tudes, see  Star  magnitudes;  system 
contrasted  with  solar,  609,  610. 

STONE,  E.  J.  (1831-97),  English  astr.,  563. 

STRUVE,  H.  (? ),  German  astr.,  450, 

459. 

SUMNER,  T.  H.  (1810-70),  American 
navigator,  113,  114. 

Sun,  the :— its  apparent  annual  motion,  23, 
155 ;  its  distance  determined  by  aber- 
ration, 173 ;  stated,  173,  223,  442,  475 ; 
diameter,  surface  and  volume,  224; 
mass,  225;  total  attraction  on  earth, 
226 ;  surface  gravity,  227 ;  density, 
228 ;  rotation  and  position  of  its  poles 
and  equator,  229 ;  equatorial  accelera- 
tion, 230;  arrangements  for  study  of 


its  surface,  231 ;  photography  of,  232 ; 
the  photosphere  and  faculae,  233,  278 ; 
spots,  234-243,  253 ;  its  spectrum,  246- 
251;  chemical  elements  detected  in, 
248-250 ;  its  reversing  layer,  252,  279 ; 
the  chromosphere  and  prominences, 
257-261,  279 ;  its  corona,  262-264,  280 ; 
its  light,  quantity,  and  intensity,  265, 
266 ;  its  heat,  quantity,  the  solar  con- 
stant, and  energy  of  radiation,  267- 
271;  effective  temperature,  272-273; 
constancy  of  its  radiation,  274;  main- 
tenance of  radiation,  275,  276;  sum- 
mary as  to  constitution,  277-280; 
eclipses  of,  289-296 ;  parabolic  velocity 
at  its  surface,  319;  the  tide-raising 

,-•  force,  335 ;  its  distance  determined  by 
constant  of  light-equation,  442:  paral- 
lax determined  by  various  methods, 
465-474-:  value  stated,  223,  475,  page 
582:  repulsive  force,  502;  its  motion 
in  space,  543;  its  stellar  magnitude, 
558;  its  probable  age  and  duration, 
618 ;  question  whether  it  has  reached 
its  maximum  of  temperature,  618, 
note. 

Sun,  central,  the,  544,  609. 

Sunlight  at  Neptune,  461. 

Sunrise  and  sunset,  time  of,  how  com- 
puted, 104. 

Sun-spots : — their  appearance,  234 ;  their 
probable  nature,  235 ;  dimensions,  236 ; 
development,  changes,  and  duration, 
237;  their  motions,  238;  their  distri- 
bution on  sun's  surface,  239;  their 
periodicity,  240;  Spoerer's  Law  of 
Sun-Spot  Latitudes,  241 ;  theories  as 
to  their  cause,  242;  terrestrial  influ- 
ences and  relation  to  magnetic  dis- 
turbances, 243;  their  spectrum,  253. 

Superior  planets,  their  motion  in  elonga- 
tion, 357. 

Surface  gravity,  on  moon,  200;  of  a 
planet,  how  determined,  382.  See  also 
Table  I,  page  583,  for  surface  gravity 
on  sun  and  planets. 

SWEDENBORG,      ElUANUEL       (1688-1772), 

Swedish  philosopher,  613. 

SWIFT,  L.  (1820 ),  American  astr., 

479,  504. 

Symbols,  miscellaneous,  page  581. 

Synodic  period  defined,  191,  351. 

System,  planetary  or  solar,  the,  stability 
of,  377 ;  Sir  John  Herschel's  illustra- 
tion of  its  scale,  389;  genesis  of,  the 
nebular  hypothesis,  612-614;  its  age 
and  duration,  618. 

System,  stellar,  question  as  to  its  nature, 
609,  610. 

System,  the  Ptolemaic,  359;  the  Coper- 
nican,  360;  the  Tychonic,  361. 

Systems,  binary,  587-595. 

Syzygy  defined,  190- 


INDEX 


609 


Table  and  diagram  showing  relation 
between  systems  of  celestial  coordi- 
nates, 29,  30;  of  names,  approximate 
period  and  distances  of  the  planets, 
350;  giving  values  of  the  distance  of 
the  sun  corresponding  to  different  val- 
ues of  its  parallax,  475;  values  of 
solar  parallax  obtained  by  different 
methods,  475,  note ;  of  telescopic  aper- 
tures required  to  show  stars  of  differ- 
ent magnitudes,  559. 

Tables  of  Appendix :  — 

I.  Planetary  data,        page        583. 
II.  Satellite  data,  "    584,  585. 

III.  Comets  of  which 

returns  have  been 

observed,  "  586. 

IV.  Stellar    parallaxes, 

distances,       and 
motions,  587. 

V.  Radial      velocities 

of  stars,  "  588. 

VI.  Variable  stars,  589. 

VII.  Binary  star  orbits,       "  590. 

VIII.  Mean  refractions,        "  591. 

Tail,  or  train,  of  comet,  492, 493,  495,  500, 
501,  502,  503;  repulsive  force  which 
produces  it,  502. 

TALCOTT,  CAPT.  A.  (1798-1883),  U.  S. 
engineer,  92,  note. 

Tebbutt's  comet  of  1881,  504. 

Telegraph,  longitude  by,  100. 

Telegraphic  method  of  time  observation, 
59. 

Telescope:  —  general  principle  of,  40; 
simple  refracting,  41;  magnifying 
power,  42 ;  light-gathering  power,  43 ; 
achromatic,  44;  reflecting,  49;  re- 
fracting and  reflecting,  compared,  51 ; 
mounting  of,  52;  view-,  of  spectro- 
scope, 244. 

Telescopes,  early  long,  44,  note;  large, 
51 ;  photographic,  536. 

Telescopic,  study  of  sun's  surface,  231 ; 
aperture  required  to  show  stars  of 
given  magnitude,  559. 

Telespectroscope,  the,  244. 

TEMPEL,  E.  W.  L.  (1821-89),  Milanese 
astr.,  526,  page  586. 

Temperature:  —  probable,  of  moon,  212; 
effective,  of  solar  surface,  272;  ques- 
tionable, of  Mars,  415;  probable,  of 
Jupiter,  437 ;  of  comets,  498 ;  of  mete- 
orites, 512;  doubtful,  of  nebulae,  603; 
probably  low,  of  the  original  nebula 
of  solar  system,  614. 

Temporary  stars,  or  "Novae,"  575-577; 
explanations  of,  581. 

Terminator,  the,  denned,  205. 

Tethys,  a  satellite  of  Saturn,  452. 

Theodolite,  astronomical,  70. 


Three  bodies,  problem  of,  322-325. 

Thule,  the  remotest  asteroid,  420. 

"  Thwartwise  "  or  "  cross  "  motion,  540. 

Tidal  evolution,  346,  614. 

Tides,  the,  330-346 ;  definitions,  330,  331  ; 
the  tide-raising  force,  332-335 ;  condi- 
tions for  a  permanent  tide,  336 ;  effect 
of  earth's  rotation  on,  337;  free  and 
forced  oscillations,  338 ;  cotidal  lines, 
339 ;  course  of  the  main  tidal  wave,  340 ; 
in  rivers,  341 ;  height  of,  342 ;  effect  of 
wind  on,  etc.,  343 ;  in  inland  lakes  and 
seas,  344;  effect  on  earth's  rotation, 
345:  effect  on  moon's  motion,  346. 

Time,  different  kinds,  95;  sidereal,  25, 
96;  apparent  solar,  97;  mean  solar, 
98;  relation  between  the  different 
kinds,  99;  methods  of  determining, 
101,  103;  local  and  standard,  110; 
equation  of,  99,  174-177. 

TISSERAND,  F.  (1845-96),  French  astr., 
386. 

Titan,  Saturn's  largest  satellite,  452. 

Titania,  third  and  largest  satellite  of 
Uranus,  456. 

TITIUS,  J.  D.  (1729-96),  German  astr.,  349. 

Torsion  balance,  148-153. 

Total  eclipses,  of  the  moon,  287 ;  and  an- 
nular of  the  sun,  290. 

Transformation  of  astronomical  coordi- 
nates, 700-702. 

Transit-circle,  see  Meridian-circle. 

Transit-instrument,  the,  described,  61; 
conditions  and  adjustments,  62,  63; 
determination  of  time  by,  101. 

Transits,  meridian,  photographic  method 
of  observation,  65;  daily,  of  moon, 
interval  between,  193;  of  Mercury, 
396;  of  Venus,  405-406;  observed  for 
solar  parallax,  469-472. 

Transparency  of  space  affected  by  mete- 
ors, 520. 

Triangle,  the  astronomical,  31. 

Tropical  year,  the,  182,  page  582. 

Tropics,  the,  156. 

TROUVELOT,  L.  (1827-95),  French-Ameri- 
can astr.,  433. 

TROWBRIDGE,  J.  (1843 ),  American 

physicist,  249. 

TURNER,  H.  H.  (? ),  English  astr., 

523. 

TUTTLE,  H.  P.  (1839 ),  American 

astr.,  526. 

Twilight,  85. 

TWINING,  A.  C.  (1801-84),  American 
physicist,  525. 

Twinkling  of  stars,  84. 

Two  bodies,  problem  of,  316,  317. 

Tycho  Brahe  (1546-1601),  Danish  astr., 
361,  481,  532,  533,  575;  lunar  crater, 
217,  219. 

Typical  stars  of  first  and  second  magni- 
tudes, 557. 


610 


MANUAL   OF    ASTRONOMY 


Ultra-Neptunian  planets,  462. 

ULUGH  BEIGH  (1394-1449),  Arabian  astr. 
(Samarcand),  533,  555,  note. 

Umbriel,  satellite  of  Uranus,  456. 

Uncertainty  of  measured  diameters,  den- 
sities, and  masses  of  some  planets,  379. 

Universal  instrument,  70. 

Universe,  stellar,  structure  of,  605-608. 

Uranometria,  Argelander's,  555 ;  of  Hip- 
parchus,  Ptolemy,  and  Ulugh  Beigh, 
555,  note;  Cambridge,  557;  Oxonien- 
sis,557,560  (1). 

Uranus,  discovery  of,  418;  the  planet, 
453-456. 

Utility  of  astronomy,  5. 


Vanadium  in  sun-spots,  253. 

Vanishing  point,  7. 

Variable  stars,  573-584 :  — classification 
of,  573 ;  non-periodic  variables,  Class  I 
(gradual),  574;  Class  II  (irregular), 
574 ;  Class  III  (temporary  or  "Novae"), 
575-577:  periodic,  Class  IV  (Mira 
type), 578;  Class  V,  short  period  (type 
of  ft  Lyrae),  579 ;  Class  VI  (Algol  type), 
580 ;  explanations  of  variability,  581 ; 
stellar  eclipses,  dimensions  of  Algol 
system,  582 ;  number  and  designation 
of  variables,  583;  discovery  by  pho- 
tography, 583 ;  variable-star  clusters, 
584 ;  table  of  principal  variables  visi- 
ble in  United  States,  page  589. 

Variation,  possible  in  length  of  day,  128, 
345;  the  lunar,  328  (5). 

Vega  (a  Lyras),  457,  560,  562,  563,  564. 

Velocities,  areal,  linear,  and  angular,  in 
central  motion,  their  relations  —  for- 
mulae, 305. 

Velocity,  orbital,  of  the  earth,  119,  173, 
223;  of  light,  173,  441,  442;  of  the 
moon's  shadow  during  a  total  solar 
eclipse,  292 ;  the  parabolic,  or  velocity 
from  infinity,  318,  319;  of  meteors, 
510, 517 ;  radial,  determination  of,  541, 
542 ;  of  sun's  motion  in  space,  543 ;  of 
spectroscopic  binaries,  592,  593 ;  Table 
of  radial  velocities  of  stars,  page 
588. 

Venus,  397-406 :  orbital  peculiarities  and 
brightness,  397 ;  diameter,  mass,  and 
density,  398;  phases,  399;  albedo, 
400;  atmosphere,  401;  unexplained 
light  on  surface,  401 ;  surface  mark- 
ings, 402;  rotation,  403;  imagined 
satellite,  404 ;  transits,  405,  406 ;  tran- 
sits observed  for  solar  parallax,  469- 
472. 

Vernal  Equinox,  or  First  of  Aries,  22,  23. 


Vertical  circles,  14, 

VERY,  F.  W.  (? ),  American  astr., 

212. 

Vesta,  asteroid,  418,  422. 

Victoria,  asteroid,  468. 

View-telescope  of  spectroscope,  244. 

Visible  horizon  defined,  13. 

Visitors,  astronomical,  to  solar  system, 
comets,  and  meteors,  489,  513. 

VOGEL,  H.  C.  (1842-1907),  German  astro- 
physicist, 393,  409,  542,  569,  575,  576, 
582,  592,  593,  Table  V,  page  588. 

Vulcan,  a  supposed  intramercurial 
planet,  429. 


W 


Washington  telescope,  faintest  stars  visi- 
ble, 559. 

Water  vapor,  absent  on  moon,  208 ;  ques- 
tion of  its  presence  on  Mercury,  393 ; 
Venus,  401;  Mars,  409. 

WATSON,  J.  C.  (1838-80),  American  astr., 
320,  321,  401,  424. 

Wave-length,  apparent,  changed  by  radial 
motion,  Doppler's  principle,  254;  by 
other  causes,  256,  542. 

Way,  the  sun's,  543. 

WEBB,  T.  W.  (1807-85),  English  ama- 
teur, 218,  220. 

Weight,  loss  of,  between  pole  and  equa- 
tor of  earth,  136 ;  distinguished  from 
mass,  140,  141. 

Whirlpool  nebula,  the,  599. 

WILLIAMS,  STANLEY  (? ),  English 

amateur,  445. 

Wind,  its  effect  on  tides,  343. 

WOLF,    MAX   (? ),    German    astr., 

419,  600. 

WOLF,  R.  (1816-93),  Swiss  astr.,  240. 

Wolf-Rayet  stars,  569. 

WOLLASTON,  W.  H.  (1766-1828),  English 
physicist,  210. 

WRIGHT,  T.  (1750),  English  amateur, 
449. 


Yale  College  Observatory,  its  heliometer, 

73. 

Y  Cygni,  peculiar  variation  of,  582. 
Year,    the    three    kinds   of,  182;    their 

respective  lengths,  182,  page  582 ;  the 

eclipse  year,  297. 
Yerkes  Observatory,  its  telescope,  43, 51, 

422,  559;    engraving  of  observatory, 

page  135 ;  photographs  of  moon,  222 ; 

its  Bruce  spectrograph,  542,  page  505 ; 

observations  of  Nichols  on  heat  from 

stars,  563 ;  photographs  of  Nova  Persei 

nebula,  577. 


INDEX 


611 


Zenith,  the  astronomical  and  geocentric, 

11. 

Zenith-distance  defined,  15. 
Zenith-telescope,  the,  92. 
Zero,  absolute,  of  temperature,  273,  note ; 

points  of  meridian-circle,  69. 


Zodiac,  the,  157. 

Zodiacal  light,  the,  430. 

ZOLLNER,  J.   C.   F.    (1834-82),   German 

astrophysicist,  210,  395,  400,  408,  433, 

446,  455,  459,  562. 
Zones,  BesseFs,  Argelander's,  Gould's, 

etc.,  533. 


14  DAY  USE 

RETURN  TO  DESK  FROM  WHICH  BORROWED 

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